**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2519

# Search results for: Strongly convex function.

##### 2519 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.

##### 2518 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.

##### 2517 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

##### 2516 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

##### 2515 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.

##### 2514 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.

##### 2513 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.

##### 2512 Strongly Screenableness and its Tychonoff Products

**Authors:**
Jianjun Wang,
Peiyong Zhu

**Abstract:**

In this paper, we prove that if X is regular strongly screenable DC-like (C-scattered), then X ×Y is strongly screenable for every strongly screenable space Y . We also show that the product i∈ω Yi is strongly screenable if every Yi is a regular strongly screenable DC-like space. Finally, we present that the strongly screenableness are poorly behaved with its Tychonoff products.

**Keywords:**
Topological game,
strongly screenable,
scattered,
Cscattered.

##### 2511 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.

##### 2510 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.

##### 2509 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.

##### 2508 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.

##### 2507 The Core and Shapley Function for Games on Augmenting Systems with a Coalition Structure

**Authors:**
Fan-Yong Meng

**Abstract:**

In this paper, we first introduce the model of games on augmenting systems with a coalition structure, which can be seen as an extension of games on augmenting systems. The core of games on augmenting systems with a coalition structure is defined, and an equivalent form is discussed. Meantime, the Shapley function for this type of games is given, and two axiomatic systems of the given Shapley function are researched. When the given games are quasi convex, the relationship between the core and the Shapley function is discussed, which does coincide as in classical case. Finally, a numerical example is given.

**Keywords:**
Cooperative game,
augmenting system,
Shapley function,
core.

##### 2506 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

##### 2505 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.

##### 2504 A Novel Multiresolution based Optimization Scheme for Robust Affine Parameter Estimation

**Authors:**
J.Dinesh Peter

**Abstract:**

**Keywords:**
Image Processing,
Affine parameter estimation,
Outliers,
Robust Statistics,
Robust M-estimators

##### 2503 n− Strongly Gorenstein Projective, Injective and Flat Modules

**Authors:**
Jianmin Xing Wei Shao

**Abstract:**

Let R be a ring and n a fixed positive integer, we investigate the properties of n-strongly Gorenstein projective, injective and flat modules. Using the homological theory , we prove that the tensor product of an n-strongly Gorenstein projective (flat) right R -module and projective (flat) left R-module is also n-strongly Gorenstein projective (flat). Let R be a coherent ring ,we prove that the character module of an n -strongly Gorenstein flat left R -module is an n-strongly Gorenstein injective right R -module . At last, let R be a commutative ring and S a multiplicatively closed set of R , we establish the relation between n -strongly Gorenstein projective (injective , flat ) R -modules and n-strongly Gorenstein projective (injective , flat ) S−1R-modules. All conclusions in this paper is helpful for the research of Gorenstein dimensions in future.

**Keywords:**
Commutative ring,
n-strongly Gorenstein projective,
n-Strongly Gorenstein injective,
n-strongly Gorenstein flat,
S-ring.

##### 2502 Adomian Method for Second-order Fuzzy Differential Equation

**Authors:**
Lei Wang,
Sizong Guo

**Abstract:**

In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.

**Keywords:**
Fuzzy-valued function,
fuzzy initial value problem,
strongly generalized differentiability,
adomian decomposition method.

##### 2501 Non-Convex Multi Objective Economic Dispatch Using Ramp Rate Biogeography Based Optimization

**Authors:**
Susanta Kumar Gachhayat,
S. K. Dash

**Abstract:**

Multi objective non-convex economic dispatch problems of a thermal power plant are of grave concern for deciding the cost of generation and reduction of emission level for diminishing the global warming level for improving green-house effect. This paper deals with ramp rate constraints for achieving better inequality constraints so as to incorporate valve point loading for cost of generation in thermal power plant through ramp rate biogeography based optimization involving mutation and migration. Through 50 out of 100 trials, the cost function and emission objective function were found to have outperformed other classical methods such as lambda iteration method, quadratic programming method and many heuristic methods like particle swarm optimization method, weight improved particle swarm optimization method, constriction factor based particle swarm optimization method, moderate random particle swarm optimization method etc. Ramp rate biogeography based optimization applications prove quite advantageous in solving non convex multi objective economic dispatch problems subjected to nonlinear loads that pollute the source giving rise to third harmonic distortions and other such disturbances.

**Keywords:**
Economic load dispatch,
Biogeography based optimization,
Ramp rate biogeography based optimization,
Valve Point loading,
Moderate random particle swarm optimization method,
Weight improved particle swarm optimization method

##### 2500 Impulse Response Shortening for Discrete Multitone Transceivers using Convex Optimization Approach

**Authors:**
Ejaz Khan,
Conor Heneghan

**Abstract:**

**Keywords:**
Equalizer,
target impulse response,
convex optimization,
matrix inequality.

##### 2499 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

##### 2498 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.

##### 2497 Labyrinth Fractal on a Convex Quadrilateral

**Authors:**
Harsha Gopalakrishnan,
Srijanani Anurag Prasad

**Abstract:**

Quadrilateral Labyrinth Fractals are a type of fractals presented in this paper. They belong to a unique class of fractals on any plane quadrilateral. The previously researched labyrinth fractals on the unit square and triangle inspire this form of fractal. This work describes how to construct a quadrilateral labyrinth fractal and looks at the circumstances in which it can be understood as the attractor of an iterated function system. Furthermore, some of its topological properties and the Hausdorff and box-counting dimensions of the quadrilateral labyrinth fractals are studied.

**Keywords:**
Fractals,
labyrinth fractals,
dendrites,
iterated function
system,
non-self similar,
non-self affine,
connected,
path connected.

##### 2496 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.

##### 2495 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.

##### 2494 Probability of Globality

**Authors:**
Eva Eggeling,
Dieter W. Fellner,
Torsten Ullrich

**Abstract:**

**Keywords:**
global optimization,
probability theory,
probability of
globality

##### 2493 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.

##### 2492 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

##### 2491 Optimal Economic Restructuring Aimed at an Increase in GDP Constrained by a Decrease in Energy Consumption and CO2 Emissions

**Authors:**
Alexander Y. Vaninsky

**Abstract:**

The objective of this paper is finding the way of economic restructuring - that is, change in the shares of sectoral gross outputs - resulting in the maximum possible increase in the gross domestic product (GDP) combined with decreases in energy consumption and CO_{2} emissions. It uses an input-output model for the GDP and factorial models for the energy consumption and CO_{2} emissions to determine the projection of the gradient of GDP, and the antigradients of the energy consumption and CO_{2} emissions, respectively, on a subspace formed by the structure-related variables. Since the gradient (antigradient) provides a direction of the steepest increase (decrease) of the objective function, and their projections retain this property for the functions' limitation to the subspace, each of the three directional vectors solves a particular problem of optimal structural change. In the next step, a type of factor analysis is applied to find a convex combination of the projected gradient and antigradients having maximal possible positive correlation with each of the three. This convex combination provides the desired direction of the structural change. The national economy of the United States is used as an example of applications.

**Keywords:**
Economic restructuring,
Input-Output analysis,
Divisia index,
Factorial decomposition,
E3 models.

##### 2490 Combination Scheme of Affine Projection Algorithm Filters with Complementary Order

**Authors:**
Young-Seok Choi

**Abstract:**

This paper proposes a complementary combination scheme of affine projection algorithm (APA) filters with different order of input regressors. A convex combination provides an interesting way to keep the advantage of APA having different order of input regressors. Consequently, a novel APA which has the rapid convergence and the reduced steady-state error is derived. Experimental results show the good properties of the proposed algorithm.

**Keywords:**
Adaptive filter,
affine projection algorithm,
convex combination,
input order.