**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3923

# Search results for: convex feasibility problem

##### 3923 Comparative Analysis of Classical and Parallel Inpainting Algorithms Based on Affine Combinations of Projections on Convex Sets

**Authors:**
Irina Maria Artinescu,
Costin Radu Boldea,
Eduard-Ionut Matei

**Abstract:**

The paper is a comparative study of two classical vari-ants of parallel projection methods for solving the convex feasibility problem with their equivalents that involve variable weights in the construction of the solutions. We used a graphical representation of these methods for inpainting a convex area of an image in order to investigate their effectiveness in image reconstruction applications. We also presented a numerical analysis of the convergence of these four algorithms in terms of the average number of steps and execution time, in classical CPU and, alternativaly, in parallel GPU implementation.

**Keywords:**
convex feasibility problem,
convergence analysis,
ınpainting,
parallel projection methods

##### 3922 Sparse-View CT Reconstruction Based on Nonconvex L1 − L2 Regularizations

**Authors:**
Ali Pour Yazdanpanah,
Farideh Foroozandeh Shahraki,
Emma Regentova

**Abstract:**

**Keywords:**
Computed tomography,
sparse-view reconstruction,
L1 −L2 minimization,
non-convex,
difference of convex functions.

##### 3921 The Algorithm to Solve the Extend General Malfatti’s Problem in a Convex Circular Triangle

**Authors:**
Ching-Shoei Chiang

**Abstract:**

The Malfatti’s problem solves the problem of fitting three circles into a right triangle such that these three 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; it is called the 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 the 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 the 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 as in Tri(Tn) problems. We call these problems the Carc(Tn) problems. The algorithm is a mO(Tn) algorithm, where m is the number of iterations in the loop. It takes less than 1000 iterations and less than 1 second for the Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties. This algorithm gives a solution for circle packing problem inside convex circular triangle with arbitrarily-sized circles. Many applications concerning circle packing may come from the result of the algorithm, such as logo design, architecture design, etc.

**Keywords:**
Circle packing,
computer-aided geometric design,
geometric constraint solver,
Malfatti’s problem.

##### 3920 Q-Learning with Eligibility Traces to Solve Non-Convex Economic Dispatch Problems

**Authors:**
Mohammed I. Abouheaf,
Sofie Haesaert,
Wei-Jen Lee,
Frank L. Lewis

**Abstract:**

Economic Dispatch is one of the most important power system management tools. It is used to allocate an amount of power generation to the generating units to meet the load demand. The Economic Dispatch problem is a large scale nonlinear constrained optimization problem. In general, heuristic optimization techniques are used to solve non-convex Economic Dispatch problem. In this paper, ideas from Reinforcement Learning are proposed to solve the non-convex Economic Dispatch problem. Q-Learning is a reinforcement learning techniques where each generating unit learn the optimal schedule of the generated power that minimizes the generation cost function. The eligibility traces are used to speed up the Q-Learning process. Q-Learning with eligibility traces is used to solve Economic Dispatch problems with valve point loading effect, multiple fuel options, and power transmission losses.

**Keywords:**
Economic Dispatch,
Non-Convex Cost Functions,
Valve Point Loading Effect,
Q-Learning,
Eligibility Traces.

##### 3919 Ranking - Convex Risk Minimization

**Authors:**
Wojciech Rejchel

**Abstract:**

The problem of ranking (rank regression) has become popular in the machine learning community. This theory relates to problems, in which one has to predict (guess) the order between objects on the basis of vectors describing their observed features. In many ranking algorithms a convex loss function is used instead of the 0-1 loss. It makes these procedures computationally efficient. Hence, convex risk minimizers and their statistical properties are investigated in this paper. Fast rates of convergence are obtained under conditions, that look similarly to the ones from the classification theory. Methods used in this paper come from the theory of U-processes as well as empirical processes.

**Keywords:**
Convex loss function,
empirical risk minimization,
empirical process,
U-process,
boosting,
euclidean family.

##### 3918 Characterizations of Star-Shaped, L-Convex, and Convex Polygons

**Authors:**
Thomas Shermer,
Godfried T. Toussaint

**Abstract:**

**Keywords:**
Convex polygons,
L-convex polygons,
star-shaped
polygons,
chords,
weak visibility,
discrete and computational
geometry

##### 3917 Neural Network in Fixed Time for Collision Detection between Two Convex Polyhedra

**Authors:**
M. Khouil,
N. Saber,
M. Mestari

**Abstract:**

In this paper, a different architecture of a collision detection neural network (DCNN) is developed. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons, linear and threshold logic, which simplified the actual implementation of all the networks proposed. The study of the collision detection is divided into two sections, the collision between a point and a polyhedron and then the collision between two convex polyhedra. The aim of this research is to determine through the AMAXNET network a mini maximum point in a fixed time, which allows us to detect the presence of a potential collision.

**Keywords:**
Collision identification,
fixed time,
convex polyhedra,
neural network,
AMAXNET.

##### 3916 A Dual Method for Solving General Convex Quadratic Programs

**Authors:**
Belkacem Brahmi,
Mohand Ouamer Bibi

**Abstract:**

In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.

**Keywords:**
Convex quadratic programming,
dual support methods,
active set methods.

##### 3915 Enhanced Interference Management Technique for Multi-Cell Multi-Antenna System

**Authors:**
Simon E. Uguru,
Victor E. Idigo,
Obinna S. Oguejiofor,
Naveed Nawaz

**Abstract:**

As the deployment of the Fifth Generation (5G) mobile communication networks take shape all over the world, achieving spectral efficiency, energy efficiency, and dealing with interference are among the greatest challenges encountered so far. The aim of this study is to mitigate inter-cell interference (ICI) in a multi-cell multi-antenna system while maximizing the spectral efficiency of the system. In this study, a system model was devised that showed a miniature representation of a multi-cell multi-antenna system. Based on this system model, a convex optimization problem was formulated to maximize the spectral efficiency of the system while mitigating the ICI. This optimization problem was solved using CVX, which is a modeling system for constructing and solving discipline convex programs. The solutions to the optimization problem are sub-optimal coordinated beamformers. These coordinated beamformers direct each data to the served user equipments (UEs) in each cell without interference during downlink transmission, thereby maximizing the system-wide spectral efficiency.

**Keywords:**
coordinated beamforming,
convex optimization,
inter-cell interference,
multi-antenna,
multi-cell,
spectral efficiency

##### 3914 Optimal Dynamic Economic Load Dispatch Using Artificial Immune System

**Authors:**
I. A. Farhat

**Abstract:**

The The dynamic economic dispatch (DED) problem is one of the complex constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand. Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better.

**Keywords:**
Artificial Immune System (AIS),
Dynamic Economic Dispatch (DED).

##### 3913 Improved Artificial Bee Colony Algorithm for Non-Convex Economic Power Dispatch Problem

**Authors:**
Badr M. Alshammari,
T. Guesmi

**Abstract:**

This study presents a modified version of the artificial bee colony (ABC) algorithm by including a local search technique for solving the non-convex economic power dispatch problem. The local search step is incorporated at the end of each iteration. Total system losses, valve-point loading effects and prohibited operating zones have been incorporated in the problem formulation. Thus, the problem becomes highly nonlinear and with discontinuous objective function. The proposed technique is validated using an IEEE benchmark system with ten thermal units. Simulation results demonstrate that the proposed optimization algorithm has better convergence characteristics in comparison with the original ABC algorithm.

**Keywords:**
Economic power dispatch,
artificial bee colony,
valve-point loading effects,
prohibited operating zones.

##### 3912 On Constructing Approximate Convex Hull

**Authors:**
M. Zahid Hossain,
M. Ashraful Amin

**Abstract:**

The algorithms of convex hull have been extensively studied in literature, principally because of their wide range of applications in different areas. This article presents an efficient algorithm to construct approximate convex hull from a set of n points in the plane in O(n + k) time, where k is the approximation error control parameter. The proposed algorithm is suitable for applications preferred to reduce the computation time in exchange of accuracy level such as animation and interaction in computer graphics where rapid and real-time graphics rendering is indispensable.

**Keywords:**
Convex hull,
Approximation algorithm,
Computational
geometry,
Linear time.

##### 3911 Optimal Dynamic Economic Load Dispatch Using Artificial Immune System

**Authors:**
I. A. Farhat

**Abstract:**

The dynamic economic dispatch (DED) problem is one of the complex constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand. Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better.

**Keywords:**
Artificial Immune System (AIS),
Dynamic Economic Dispatch (DED).

##### 3910 A Numerical Algorithm for Positive Solutions of Concave and Convex Elliptic Equation on R2

**Authors:**
Hailong Zhu,
Zhaoxiang Li

**Abstract:**

In this paper we investigate numerically positive solutions of the equation -Δu = λuq+up with Dirichlet boundary condition in a boundary domain ╬® for λ > 0 and 0 < q < 1 < p < 2*, we will compute and visualize the range of λ, this problem achieves a numerical solution.

**Keywords:**
positive solutions,
concave-convex,
sub-super solution method,
pseudo arclength method.

##### 3909 Certain Conditions for Strongly Starlike and Strongly Convex Functions

**Authors:**
Sukhwinder Singh Billing,
Sushma Gupta,
Sukhjit Singh Dhaliwal

**Abstract:**

**Keywords:**
Analytic function,
Multiplier transformation,
Strongly starlike function,
Strongly convex function.

##### 3908 Improved Exponential Stability Analysis for Delayed Recurrent Neural Networks

**Authors:**
Miaomiao Yang,
Shouming Zhong

**Abstract:**

This paper studies the problem of exponential stability analysis for recurrent neural networks with time-varying delay.By establishing a suitable augmented LyapunovCKrasovskii function and a novel sufficient condition is obtained to guarantee the exponential stability of the considered system.In order to get a less conservative results of the condition,zero equalities and reciprocally convex approach are employed. The several exponential stability criterion proposed in this paper is simpler and effective. A numerical example is provided to demonstrate the feasibility and effectiveness of our results.

**Keywords:**
Exponential stability ,
Neural networks,
Linear matrix inequality,
Lyapunov-Krasovskii,
Time-varying.

##### 3907 Stability Criteria for Uncertainty Markovian Jumping Parameters of BAM Neural Networks with Leakage and Discrete Delays

**Authors:**
Qingqing Wang,
Baocheng Chen,
Shouming Zhong

**Abstract:**

In this paper, the problem of stability criteria for Markovian jumping BAM neural networks with leakage and discrete delays has been investigated. Some new sufficient condition are derived based on a novel Lyapunov-Krasovskii functional approach. These new criteria based on delay partitioning idea are proved to be less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, one numerical example is given to illustrate the the usefulness and feasibility of the proposed main results.

**Keywords:**
Stability,
Markovian jumping neural networks,
Timevarying
delays,
Linear matrix inequality.

##### 3906 Improved Stability Criteria for Neural Networks with Two Additive Time-Varying Delays

**Authors:**
Miaomiao Yang,
Shouming Zhong

**Abstract:**

This paper studies the problem of stability criteria for neural networks with two additive time-varying delays.A new Lyapunov-Krasovskii function is constructed and some new delay dependent stability criterias are derived in the terms of linear matrix inequalities(LMI), zero equalities and reciprocally convex approach.The several stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.

**Keywords:**
Stability,
Neural networks,
Linear Matrix Inequalities
(LMI) ,
Lyapunov function,
Time-varying delays

##### 3905 On a New Numerical Analysis for the Symmetric Shortest Queue Problem

**Authors:**
Tayeb Lardjane,
Rabah Messaci

**Abstract:**

We consider a network of two M/M/1 parallel queues having the same poisonnian arrival stream with rate λ. Upon his arrival to the system a customer heads to the shortest queue and stays until being served. If the two queues have the same length, an arriving customer chooses one of the two queues with the same probability. Each duration of service in the two queues is an exponential random variable with rate μ and no jockeying is permitted between the two queues. A new numerical method, based on linear programming and convex optimization, is performed for the computation of the steady state solution of the system.

**Keywords:**
Steady state solution,
matrix formulation,
convex set,
shortest queue,
linear programming.

##### 3904 An Efficient Stud Krill Herd Framework for Solving Non-Convex Economic Dispatch Problem

**Authors:**
Bachir Bentouati,
Lakhdar Chaib,
Saliha Chettih,
Gai-Ge Wang

**Abstract:**

The problem of economic dispatch (ED) is the basic problem of power framework, its main goal is to find the most favorable generation dispatch to generate each unit, reduce the whole power generation cost, and meet all system limitations. A heuristic algorithm, recently developed called Stud Krill Herd (SKH), has been employed in this paper to treat non-convex ED problems. The proposed KH has been modified using Stud selection and crossover (SSC) operator, to enhance the solution quality and avoid local optima. We are demonstrated SKH effects in two case study systems composed of 13-unit and 40-unit test systems to verify its performance and applicability in solving the ED problems. In the above systems, SKH can successfully obtain the best fuel generator and distribute the load requirements for the online generators. The results showed that the use of the proposed SKH method could reduce the total cost of generation and optimize the fulfillment of the load requirements.

**Keywords:**
Stud Krill Herd,
economic dispatch,
crossover,
stud selection,
valve-point effect.

##### 3903 Design of a Reduced Order Robust Convex Controller for Flight Control System

**Authors:**
S. Swain,
P. S. Khuntia

**Abstract:**

In this paper an optimal convex controller is designed to control the angle of attack of a FOXTROT aircraft. Then the order of the system model is reduced to a low-dimensional state space by using Balanced Truncation Model Reduction Technique and finally the robust stability of the reduced model of the system is tested graphically by using Kharitonov rectangle and Zero Exclusion Principle for a particular range of perturbation value. The same robust stability is tested theoretically by using Frequency Sweeping Function for robust stability.

**Keywords:**
Convex Optimization,
Kharitonov Stability Criterion,
Model Reduction,
Robust Stability.

##### 3902 Improved Robust Stability Criteria of a Class of Neutral Lur’e Systems with Interval Time-Varying Delays

**Authors:**
Longqiao Zhou,
Zixin Liu,
Shu Lü

**Abstract:**

This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.

**Keywords:**
Lur’e system,
Convex function,
Jensen integral inequality,
Triple-integral method,
Exponential stability.

##### 3901 Exponential Stability Analysis for Uncertain Neural Networks with Discrete and Distributed Time-Varying Delays

**Authors:**
Miaomiao Yang,
Shouming Zhong

**Abstract:**

This paper studies the problem of exponential stability analysis for uncertain neural networks with discrete and distributed time-varying delays. Together with a suitable augmented Lyapunov Krasovskii function, zero equalities, reciprocally convex approach and a novel sufficient condition to guarantee the exponential stability of the considered system. The several exponential stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.

**Keywords:**
Exponential stability,
Uncertain Neural networks,
LMI approach,
Lyapunov-Krasovskii function,
Time-varying.

##### 3900 Robot Path Planning in 3D Space Using Binary Integer Programming

**Authors:**
Ellips Masehian,
Golnaz Habibi

**Abstract:**

**Keywords:**
3D C-space,
Binary Integer Programming (BIP),
Delaunay Tessellation,
Robot Motion Planning.

##### 3899 Improvement of New Government R&D Program Plans through Preliminary Feasibility Studies

**Authors:**
Hyun-Kyu Kang

**Abstract:**

**Keywords:**
Preliminary feasibility study,
Government R&D program.

##### 3898 Convex Restrictions for Outage Constrained MU-MISO Downlink under Imperfect Channel State Information

**Authors:**
A. Preetha Priyadharshini,
S. B. M. Priya

**Abstract:**

In this paper, we consider the MU-MISO downlink scenario, under imperfect channel state information (CSI). The main issue in imperfect CSI is to keep the probability of each user achievable outage rate below the given threshold level. Such a rate outage constraints present significant and analytical challenges. There are many probabilistic methods are used to minimize the transmit optimization problem under imperfect CSI. Here, decomposition based large deviation inequality and Bernstein type inequality convex restriction methods are used to perform the optimization problem under imperfect CSI. These methods are used for achieving improved output quality and lower complexity. They provide a safe tractable approximation of the original rate outage constraints. Based on these method implementations, performance has been evaluated in the terms of feasible rate and average transmission power. The simulation results are shown that all the two methods offer significantly improved outage quality and lower computational complexity.

**Keywords:**
Imperfect channel state information,
outage probability,
multiuser- multi input single output.

##### 3897 Extremal Properties of Generalized Class of Close-to-convex Functions

**Authors:**
Norlyda Mohamed,
Daud Mohamad,
Shaharuddin Cik Soh

**Abstract:**

**Keywords:**
Argument of f ′(z) ,
Carathéodory Function,
Closeto-
convex Function,
Distortion Theorem,
Extremal Properties

##### 3896 A Constructive Proof of the General Brouwer Fixed Point Theorem and Related Computational Results in General Non-Convex sets

**Authors:**
Menglong Su,
Shaoyun Shi,
Qing Xu

**Abstract:**

In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.

**Keywords:**
interior path following method,
general Brouwer fixed
point theorem,
non-convex sets,
globally convergent algorithm

##### 3895 Laminar Impinging Jet Heat Transfer for Curved Plates

**Authors:**
A. M. Tahsini,
S. Tadayon Mousavi

**Abstract:**

**Keywords:**
Concave,
Convex,
Heat transfer,
Impinging jet,
Laminar flow.

##### 3894 Enhanced Particle Swarm Optimization Approach for Solving the Non-Convex Optimal Power Flow

**Authors:**
M. R. AlRashidi,
M. F. AlHajri,
M. E. El-Hawary

**Abstract:**

**Keywords:**
Particle Swarm Optimization,
Optimal Power Flow,
Economic Dispatch.