Search results for: potential problem

Authors: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: Andres Manuel Garcia Lamparte, Rocio Losada Iglesias, Marcos BoullóN Magan, David Miranda Barros

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The biodiversity strategy of the European Union for 2030, mentions climate change as one of the key factors for biodiversity loss and considers green infrastructure as one of the solutions to this problem. In this line, the European Commission has developed a green infrastructure strategy which commits members states to consider green infrastructure in their territorial planning. This green infrastructure is aimed at granting the provision of a wide number of ecosystem services to support biodiversity and human well-being by countering the effects of climate change. Yet, there are not too many tools available to delimit green infrastructure. The available ones consider the potential of the territory to provide ecosystem services. However, these methods usually aggregate several maps of ecosystem services potential without considering possible trade-offs. This can lead to excluding areas with a high potential for providing ecosystem services which have many trade-offs with other ecosystem services. In order to tackle this problem, a methodology is proposed to consider ecosystem services trade-offs in the objective function of a simulated annealing algorithm aimed at delimiting green infrastructure multifunctional buffer areas. To this end, the provision potential maps of the regulating ecosystem services considered to delimit the multifunctional buffer areas are clustered in groups, so that ecosystem services that create trade-offs are excluded in each group. The normalized provision potential maps of the ecosystem services in each group are added to obtain a potential map per group which is normalized again. Then the potential maps for each group are combined in a raster map that shows the highest provision potential value in each cell. The combined map is then used in the objective function of the simulated annealing algorithm. The algorithm is run both using the proposed methodology and considering the ecosystem services individually. The results are analyzed with spatial statistics and landscape metrics to check the number of ecosystem services that the delimited areas produce, as well as their regularity and compactness. It has been observed that the proposed methodology increases the number of ecosystem services produced by delimited areas, improving their multifunctionality and increasing their effectiveness in preventing climate change impacts.

Keywords: ecosystem services trade-offs, green infrastructure delineation, multifunctional buffer areas, climate change

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Authors: John McNamara

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Growing up creative is an important idea in today’s classrooms. As education seeks to prepare children for their futures, it is important that the system considers traditional as well as non-traditional pathways. This poster describes the findings of a research study investigating creative potential in children with learning disabilities. Children with learning disabilities were administered the Torrance Test of Creative Problem Solving along with subtests from the Comprehensive Test of Phonological Processing. A quantitative comparative analysis was computed using paired-sample t-tests. Results indicated statistically significant difference between children’s creative problem-solving skills and their reading-based skills. The results lend support to the idea that children with learning disabilities have inherent strengths in the area of creativity. It can be hypothesized that the success of these children may be associated with the notion that they are using a type of neurological processing that is not otherwise used in academic tasks. Children with learning disabilities, a presumed left-side neurological processing problem, process information with the right side of the brain – even with tasks that should be processed with the left side (i.e. language). In over-using their right hemisphere, it is hypothesized that children with learning disabilities have well-developed right hemispheres and, as such, have strengths associated with this type of processing, such as innovation and creativity. The current study lends support to the notion that children with learning disabilities may be particularly primed to succeed in areas that call on creativity and creative thinking.

Keywords: learning disabilities, educational psychology, education, creativity

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Authors: Ching-Shoei Chiang

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The Malfatti’s Problem solves the problem of fitting 3 circles into a right triangle such that these 3 circles are tangent to each other, and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles inside the triangle with special tangency properties among circles and triangle sides; we call it extended general Malfatti’s problem. In the extended general Malfatti’s problem, call it Tri(Tn), where Tn is the triangle number, there are closed-form solutions for Tri(T₁) (inscribed circle) problem and Tri(T₂) (3 Malfatti’s circles) problem. These problems become more complex when n is greater than 2. In solving Tri(Tn) problem, n>2, algorithms have been proposed to solve these problems numerically. With a similar idea, this paper proposed an algorithm to find the radii of circles with the same tangency properties. Instead of the boundary of the triangle being a straight line, we use a convex circular arc as the boundary and try to find Tn circles inside this convex circular triangle with the same tangency properties among circles and boundary Carc. We call these problems the Carc(Tn) problems. The CPU time it takes for Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties, is less than one second.

Keywords: circle packing, computer-aided geometric design, geometric constraint solver, Malfatti’s problem

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Authors: Martin Hewing, Katharina Hölzle

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Organizations increasingly use environmental stimuli and ideas from users within participatory innovation processes in order to tap new sources of knowledge. The research presented in this article focuses on users who shape the distant edges of markets and currently are not using products and services from a domain– so called potential users. Those users at the peripheries are perceived to contribute more novel information, by which they better reflect shifts in needs and behavior than current users in the core market. Their contributions in collaborative and creative problem-solving processes and how they generate ideas for discontinuous innovations are of particular interest. With an experimental design, we compare ideas from potential and current users and analyze the effects of cognitive distance in collaboration and the utilization of explicit and tacit knowledge. We find potential users to generate more original ideas, particularly when they collaborate with someone experienced within the domain. Their ideas are most obviously characterized by an increased level of surprise and unusualness compared to dominant designs, which is rooted in contexts and does not require technological leaps. Collaboration with potential users can therefore result in new ways to leverage technological competences. Furthermore, the cross-fertilization arising from cognitive distance between a potential and a current user is asymmetric due to differences in the nature of their utilized knowledge and personal objectives. This paper discusses implications for innovation research and the management of early innovation processes.

Keywords: user collaboration, co-creation, discontinuous innovation, innovation research

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Authors: Noppadon Phumeechanya, Panita Wannapiroon

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The purpose of this research is to design the ubiquitous scaffold learning environment using problem-based learning activities that enhance problem-solving skills and context awareness, and to evaluate the suitability of the ubiquitous scaffold learning environment using problem-based learning activities. We divide the research procedures into two phases. The first phase is to design the ubiquitous scaffold learning environment using problem-based learning activities, and the second is to evaluate the ubiquitous scaffold learning environment using problem-based learning activities. The sample group in this study consists of five experts selected using the purposive sampling method. We analyse data by arithmetic mean and standard deviation. The research findings are as follows; the ubiquitous scaffold learning environment using problem-based learning activities consists of three major steps, the first is preparation before learning. This prepares learners to acknowledge details and learn through u-LMS. The second is the learning process, where learning activities happen in the ubiquitous learning environment and learners learn online with scaffold systems for each step of problem solving. The third step is measurement and evaluation. The experts agree that the ubiquitous scaffold learning environment using problem-based learning activities is highly appropriate.

Keywords: ubiquitous learning environment scaffolding, learning activities, problem-based learning, problem-solving skills, context awareness

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Authors: Serhat Tüzün, Tufan Demirel

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The objective of the present study is to select the most suitable location for a wind power plant station through Choquet integral method. The problem of selecting the location for a wind power station was considered as a multi-criteria decision-making problem. The essential and sub-criteria were specified and location selection was expressed in a hierarchic structure. Among the main criteria taken into account in this paper are wind potential, technical factors, social factors, transportation, and costs. The problem was solved by using different approaches of Choquet integral and the best location for a wind power station was determined. Then, the priority weights obtained from different Choquet integral approaches are compared and commented on.

Keywords: multi-criteria decision making, choquet integral, fuzzy sets, location of a wind power plant

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Authors: Mohammad Reza Shojaei, Mahdeih Mirzaeinia

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We have studied the cluster structure of even-even stable isotopes of Ge and Sr. The Schrodinger equation has been solved using the generalized parametric Nikiforov-Uvarov method with a phenomenological potential. This potential is the sum of the attractive Yukawa-like potential, a Manning-Rosen-type potential, and the repulsive Yukawa potential for interaction between the cluster and the core. We have shown that the available experimental data of the first rotational band energies can be well described by assuming a binary system of the α cluster and the core and using an analytical solution. Our results were consistent with experimental values. Hence, this model can be applied to study the other even-even isotopes

Keywords: cluser model, NU method, ge and Sr, potential central

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Authors: Kamariah Abu Bakar, Jennifer Way

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This study investigated how young children (six years old) constructed and used representations in mathematics classroom; particularly in problem solving. The purpose of this study is to explore the ways children used representations in solving addition problems and to determine whether their representations can play a supportive role in understanding the problem situation and solving them correctly. Data collection includes observations, children’s artifact, photographs and conversation with children during task completion. The results revealed that children were able to construct and use various representations in solving problems. However, they have certain preferences in generating representations to support their problem solving.

Keywords: young children, representations, addition, problem solving

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Authors: Liudmyla Koliechkina, Olena Dvirna

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The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: discrete set, linear combinatorial optimization, multi-objective optimization, Pareto solutions, partial permutation set, structural graph

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Authors: Oktia Woro Kasmini Handayani, Sri Ratna Rahayu, Efa Nugroho, Bertakalswa Hermawati

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The double burden of nutrition problem must be faced by Indonesia as developing country. The implemented program did not improve the nutritional status, therefore need to consider to utilize local potential. The objective of this research was to find out the effectivity of magnification model of early detect through local potential utilization in urban region, Semarang, Central Java, Indonesia. The research used an experimental design with the quantitative-qualitative approach. The population was all toddlers under five within the research region, sample determination by purposive sampling, as many as 216 toddlers. Quantitative data analysis used effectively criteria by Sugiono. Qualitative data was analyzed using NVivo. The optimization of local potential in the effort of nutrition status improvement shows number of nutrition case found was increased 225% (very effective), number of cases treated was increased 175% (very effective), number of cases counselled was increased 200% (effective), and number of cases that have improvement increase 75% (effective). The local potential need to be utilized in the effort of nutrition program improvement one of it is through the community empowerment, particularly health care and health high education institution as partner.

Keywords: early detection, nutrition status, local potential, health cadre

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Authors: M. G. M. Khan, V. D. Prasad, D. K. Rao

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In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

Keywords: auxiliary variable, dynamic programming technique, nonlinear programming problem, optimum stratification, uniform distribution

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Authors: Guilherme Baldo Carlos

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The flexible job-shop scheduling problem (FJSP) is an NP-hard combinatorial optimization problem, which can be applied to model several applications in a wide array of industries. This problem will have its importance increase due to the shift in the production mode that modern society is going through. The demands are increasing and for products personalized and customized. This work aims to apply a meta-heuristic called a genetic algorithm (GA) to solve this problem. A GA is a meta-heuristic inspired by the natural selection of Charles Darwin; it produces a population of individuals (solutions) and selects, mutates, and mates the individuals through generations in order to find a good solution for the problem. The results found indicate that the GA is suitable for FJSP solving.

Keywords: genetic algorithm, evolutionary algorithm, scheduling, flexible job-shop scheduling

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Authors: Laissa Mae Francisco, John Rolex Ingreso, Anna Krizel Menguito, Criselda Robrigado, Rej Maegan Tuazon

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This study aims to determine and describe the existing relationship between number sense proficiency and problem-solving performance of grade seven students from Victorino Mapa High School, Manila. A paper pencil exam containing of 50-item number sense test and 5-item problem-solving test which measures their number sense proficiency and problem-solving performance adapted from McIntosh, Reys, and Bana were used as the research instruments. The data obtained from this study were interpreted and analyzed using the Pearson – Product Moment Coefficient of Correlation to determine the relationship between the two variables. It was found out that students who were low in number sense proficiency tend to be the students with poor problem-solving performance and students with medium number sense proficiency are most likely to have an average problem-solving performance. Likewise, students with high number sense proficiency are those who do excellently in problem-solving performance.

Keywords: number sense, performance, problem solving, proficiency

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Authors: Pei Chin Lim

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School of Mathematics and Science of Singapore Polytechnic offers a Basic Mathematics module to students who did not pass GCE O-Level Additional Mathematics. These students are weaker in Mathematics. In particular, they struggle with word problems and tend to leave them blank in tests and examinations. In order to improve students’ problem-solving skills, the school redesigned the Basic Mathematics module to incorporate Polya’s problem-solving methodology. During tutorial lessons, students have to work through learning activities designed to raise their metacognitive awareness by following Polya’s problem-solving process. To assess the effectiveness of the redesign, students’ working for a challenging word problem in the mid-semester test were analyzed. Sixty-five percent of students attempted to understand the problem by making sketches. Twenty-eight percent of students went on to devise a plan and implement it. Only five percent of the students still left the question blank. These preliminary results suggest that with regular exposure to an explicit and systematic problem-solving approach, weak students’ problem-solving skills can potentially be improved.

Keywords: mathematics education, metacognition, problem solving, weak students

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Authors: Derkaoui Orkia, Lehireche Ahmed

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The topic of this article is to exploring the potentialities of a powerful optimization technique, namely Semidefinite Programming, for solving NP-hard problems. This approach provides tight relaxations of combinatorial and quadratic problems. In this work, we solve the maximum clique problem using this relaxation. The clique problem is the computational problem of finding cliques in a graph. It is widely acknowledged for its many applications in real-world problems. The numerical results show that it is possible to find a maximum clique in polynomial time, using an algorithm based on semidefinite programming. We implement a primal-dual interior points algorithm to solve this problem based on semidefinite programming. The semidefinite relaxation of this problem can be solved in polynomial time.

Keywords: semidefinite programming, maximum clique problem, primal-dual interior point method, relaxation

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Authors: Mehmet Hakan Karaata

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In this paper, we first coin a new graph theocratic problem with numerous applications. Second, we provide two algorithms for the problem. The first solution is using a brute-force techniques, whereas the second solution is based on an initial identification of the cycles in the given graph. We then provide a correctness proof of the algorithm. The applications of the problem include graph analysis, graph drawing and network structuring.

Keywords: algorithm, cycle, graph algorithm, graph theory, network structuring

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Authors: Seyedmirsajad Mokhtarimousavi, Danial Talebi, Hamidreza Asgari

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Assigning aircrafts’ activities to appropriate gates is one the most challenging issues in airport authorities’ multiple criteria decision making. The potential financial loss due to imbalances of demand and supply in congested airports, higher occupation rates of gates, and the existing restrictions to expand facilities provide further evidence for the need for an optimal supply allocation. Passengers walking distance, towing movements, extra fuel consumption (as a result of awaiting longer to taxi when taxi conflicts happen at the apron area), etc. are the major traditional components involved in GAP models. In particular, the total cost associated with gate assignment problem highly depends on the airport terminal layout. The study herein presents a well-elaborated literature review on the topic focusing on major concerns, applicable variables and objectives, as well as proposing a three-objective mathematical model for the gate assignment problem. The model has been tested under different concourse layouts in order to check its performance in different scenarios. Results revealed that terminal layout pattern is a significant parameter in airport and that the proposed model is capable of dealing with key constraints and objectives, which supports its practical usability for future decision making tools. Potential solution techniques were also suggested in this study for future works.

Keywords: airport management, terminal layout, gate assignment problem, mathematical modeling

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Authors: Hashini E. Mohottala

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We report the combine use of Wikispaces (WikiS) and Group Problem Solving (GPS) sessions conducted in the introductory level physics classes. As a part of this new teaching tool, some essay type problems were posted on the WikiS in weekly basis and students were encouraged to participate in problem solving without providing numerical final answers but the steps. Wikispace is used as a platform for students to meet online and create discussions. Each week students were further evaluated on problem solving skills opening up more opportunity for peer interaction through GPS. Each group was given a different problem to solve and the answers were graded. Students developed a set of skills in decision-making, problem solving, communication, negotiation, critical and independent thinking and teamwork through the combination of WikiS and GPS.

Keywords: group problem solving (GPS), wikispace (WikiS), physics education, learning

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Authors: Sourabh Joshi, Tarun Sharma, Anurag Sharma

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Ant Colony Optimization is heuristic Algorithm which has been proven a successful technique applied on number of combinatorial optimization problems. Two variants of Ant Colony Optimization algorithm named Ant System and Max-Min Ant System are implemented in MATLAB to solve travelling Salesman Problem and the results are compared. In, this paper both systems are analyzed by solving the some Travelling Salesman Problem and depict which system solve the problem better in term of cost and time.

Keywords: Ant Colony Optimization, Travelling Salesman Problem, Ant System, Max-Min Ant System

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Authors: Boris Melnikov, Dmitrii Chaikovskii, Elena Melnikova

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The traveling salesman problem (TSP) is a well-known optimization problem that seeks to find the shortest possible route that visits a set of points and returns to the starting point. In this paper, we apply some heuristics of the TSP for the task of restoring the DNA matrix. This restoration problem is often considered in biocybernetics. For it, we must recover the matrix of distances between DNA sequences if not all the elements of the matrix under consideration are known at the input. We consider the possibility of using this method in the testing of distance calculation algorithms between a pair of DNAs to restore the partially filled matrix.

Keywords: optimization problems, DNA matrix, partially filled matrix, traveling salesman problem, heuristic algorithms

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Authors: Ghorbanali Mohammadi

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New approaches to sequencing mixed-model manufacturing systems are present. These approaches have attracted considerable attention due to their potential to deal with difficult optimization problems. This paper presents Multi-Objective Simulated Annealing Algorithms (MOSAA) approaches to the Just-In-Time (JIT) sequencing problem where workload-smoothing (WL) and the number of set-ups (St) are to be optimized simultaneously. Mixed-model assembly lines are types of production lines where varieties of product models similar in product characteristics are assembled. Moreover, this type of problem is NP-hard. Two annealing methods are proposed to solve the multi-objective problem and find an efficient frontier of all design configurations. The performances of the two methods are tested on several problems from the literature. Experimentation demonstrates the relative desirable performance of the presented methodology.

Keywords: scheduling, just-in-time, mixed-model assembly line, sequencing, simulated annealing

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Authors: Laila Montaser, Hala Gabr, Maha El-Bassuony, Gehan Tawfeek

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Orthotropic liver transplantation (OLT) is the final procedure of both end stage and metabolic liver diseases. Hepatocyte transplantation is an alternative for OLT, but the sources of hepatocytes are limited. Bone marrow mesenchymal stem cells (BM-MSCs) can differentiate into hepatocyte-like cells and are a potential alternative source for hepatocytes. The MSCs from bone marrow are a promising target population as they are capable of differentiating along multiple lineages and, at least in vitro, have significant expansion capability. MSCs from bone marrow may have the potential to differentiate in vitro and in vivo into hepatocytes. Our study examined whether mesenchymal stem cells (MSCs), which are stem cells originated from human bone marrow, are able to differentiate into functional hepatocyte-like cells in vitro. Our aim was to investigate the differentiation potential of BM-MSCs into hepatocyte-like cells. Adult stem cell therapy could solve the problem of degenerative disorders, including liver disease.

Keywords: bone marrow, differentiation, hepatocyte, stem cells

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Authors: Terence Soule, Tami Al Ghamdi

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To study how to transfer knowledge from multiple source problems to the target problem, we modeled the Transfer Learning (TL) process using Genetic Algorithms as the model solver. TL is the process that aims to transfer learned data from one problem to another problem. The TL process aims to help Machine Learning (ML) algorithms find a solution to the problems. The Genetic Algorithms (GA) give researchers access to information that we have about how the old problem is solved. In this paper, we have five different source problems, and we transfer the knowledge to the target problem. We studied different scenarios of the target problem. The results showed combined knowledge from multiple source problems improves the GA performance. Also, the process of combining knowledge from several problems results in promoting diversity of the transferred population.

Keywords: transfer learning, genetic algorithm, evolutionary computation, source and target

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Authors: Ocotlán Díaz-Parra, Jorge A. Ruiz-Vanoye, Alejandro Fuentes-Penna, Beatriz Bernabe-Loranca, Patricia Ambrocio-Cruz, José J. Hernández-Flores

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The Maritime Platform Transport Problem of Solid, Special and Dangerous Waste consist of to minimize the monetary value of carry different types of waste from one location to another location using ships. We offer a novel mathematical, the characterization of the problem and the use CPLEX to find the optimal values to solve the Solid, Special and Hazardous Waste Transportation Problem of offshore platforms instances of Mexican state-owned petroleum company (PEMEX). The set of instances used are WTPLib real instances and the tool CPLEX solver to solve the MPTPSSDW problem.

Keywords: oil platform, transport problem, waste, solid waste

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Authors: Thanawit Tongmai, Chatchawan Saewor

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Learning management is very important for students’ development. To promote students’ potential, the teacher should design appropriate learning activity that brings their students potential out. Problem based learning has been using worldwide and it has presented numerous of success. This research aims to study third year students’ attitude and their achievement in scientific research course. To find the results, mix method was used to design research conduction. The researcher used PBL and reflection activity in the class. The students had to choose a topic, reviewed information, designed experimental, wrote academic report and presented their research by themselves. The researcher was only a facilitator. Reflection activity was used to progressing and consulting their research. The data was collected along with research conduction by questionnaire and test, including attitude, opinion and their achievement. The result of this study showed that 74.71% from all of students (n = 87) benefited from PBL and reflection activity, while 25.19% were just satisfied. 100% of students had a positive reflection toward PBL activity and they believed that PBL was the best pedagogy method for scientific research course. The achievements of these students were higher than the previous study (P < 0.05). The student’s learning achievement, A, B+ and B, was 48.28, 28.74 and 22.98% respectively. Therefore, it can conclude that PBL activity is appropriate for scientific research course and it can also promote student’s achievement.

Keywords: reflection, attitude, learning, achievement, PBL

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Authors: Kalpana Dahiya

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This paper discusses a two-level hierarchical time minimization transportation problem, which is an important class of transportation problems arising in industries. This problem has been studied by various researchers, and a number of polynomial time iterative algorithms are available to find its solution. All the existing algorithms, though efficient, have some shortcomings. The current study proposes an alternate solution algorithm for the problem that is more efficient in terms of computational time than the existing algorithms. The results justifying the underlying theory of the proposed algorithm are given. Further, a detailed comparison of the computational behaviour of all the algorithms for randomly generated instances of this problem of different sizes validates the efficiency of the proposed algorithm.

Keywords: global optimization, hierarchical optimization, transportation problem, concave minimization

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Authors: Farzaneh Rajabighamchi, Stan van Hoesel, Christof Defryn

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The generalized traveling salesman problem (GTSP) is an extension of the traveling salesman problem (TSP) where the set of nodes is partitioned into clusters, and the salesman must visit exactly one node per cluster. In this research, we apply the definition of the GTSP to an order picker routing problem with multiple locations per product. As such, each product represents a cluster and its corresponding nodes are the locations at which the product can be retrieved. To pick a certain product item from the warehouse, the picker needs to visit one of these locations during its pick tour. As all products are scattered throughout the warehouse, the product clusters not separated geographically. We propose an exact LP model as well as heuristic and meta-heuristic solution algorithms for the order picking problem with multiple product locations.

Keywords: warehouse optimization, order picking problem, generalised travelling salesman problem, heuristic algorithm

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Authors: Ivan Baravy

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Interpolation problem, as it was initially posed in terms of polynomials, is well researched. However, further mathematical developments extended it significantly. Trigonometric interpolation is widely used in Fourier analysis, while its generalized representation as exponential interpolation is applicable to such problem of mathematical physics as modelling of Ziegler-Biersack-Littmark repulsive interatomic potentials. Formulated for finite fields, this problem arises in decoding Reed--Solomon codes. This paper shows the relation between different interpretations of the problem through the class of matrices of special structure - Hankel matrices.

Keywords: Berlekamp-Massey algorithm, exponential interpolation, finite fields, Hankel matrices, Hankel polynomials

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Authors: Mahmoud Lot

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In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Split Bregman Method, optimal control with elliptic partial differential equation constraint, finite element method

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