Sharif Digital Repository

In some cases, Mehrotra’s predictor–corrector algorithm might make very small steps in order to keep the iterate in a certain neighborhood of the central path, and thus implying the inefficiency of the algorithm. In this study, a different approach for controlling the iterates on the algorithm is investigated, which was recently introduced by Salahi and Terlaky. The approach is based on postponing the choice of the barrier parameter. To do so, a step size is fixed in the corrector step and then by solving a one dimensional optimization problem, the barrier parameter is computed. Finally, using the computed barrier parameter, the next step is taken. It has already been proved that the new... 

We describe two modified secant equations proposed by Yuan, Li and Fukushima. First, we study the approach proposed by Andrei. Then, we explain two hybrid conjugate gradient methods for unconstrained optimization problems. The methods are hybridizations of Hestenes-Stiefel and Dai-Yuan conjugate gradient methods. It is shown that one of the algorithms is globally convergent for uniformly convex functions and the other is globally convergent for general functions. Two approaches for computing the initial value of the steplength proposed by Babaie, Fatemi, and Mahdavi-Amiri and Andrei are used for accelerating the performance of the line search. We implement the algorithms and compare the... 

In order to achieve a compromised solution for a multi-objective problem, we make use of the Tchebycheff norm to minimize the distance from the current estimate of the objectives from the ideal point. Solutions obtained from the Tchebycheff approach are weakly efficient for multi-objective problems. For a better solution, the augmented weighted Tchebycheff norm has been proposed. Here, we use the satisficing tradeoff algorithm to solve the augmented weighted Tchebycheff problems. Since the supplier selection problem is usually a multi objective problem, we use the augmented weighted Tchebycheff method for obtaining its solutions. Numerical results are presented illustrating the performance... 

Automatic recognition of input characters and distinguishing image similarities have been of high interest specially as computer systems have become widely popular in industries and businesses. In this thesis, we present a method based on the Frechet distance for automatic character and image recognition. Frechet distance is a measure of similarity between polygon curves. The presented approach in this thesis is based on the work of Maheshvari,et.al.We first provide a literature review on the existing techniques, emphasizing the superior performance of rule-based algorithms, and introducing the different types of Frechet distances based on the characteristics of the input geometry. Then, we... 

Nowadays, solving large-scale unconstrained optimization problems has wide applications in data science and machine learning. Therefore, the development and analysis of efficient algorithms for solving unconstrained optimization problems is of great interest. Line search and trust region are two general frameworks for guaranteeing the convergence of algorithms for solving unconstrained optimization problems. Conjugate gradient (CG) methods and the conjugate residual (CR) balance by Hestenes and Stiefel, have been presented for solving linear systems with symmetric and positive definite coefficient matrices. The basic feature of CR, that is, residual minimization, is important and can be used... 

In recent years, stochastic-flow networks (SFNs) have been extensively applied to many problems such as distribution, power transmission, and telecommunication. In quality management and decision making, an important task is to design some performance indices in order to measure the performance of an SFN. The system reliability and unreliability are such two common performance indices.Hitherto, several research works have been conducted for evaluating these two performance indices.One approach for evaluating the reliability of SFNs is determining all the upper or lower boundary points (respectively, UBPs or LBPs).Here, we study four problems to determine: (1) all the UBPs in a two-terminal... 

We consider the problem of optimal control of switched systems. In order to solve this problem, by using the Lagrange interpolation, we transform it into an equivalent nonlocal optimal control problem, and then by applying several conditions we transform it into a moment problem. This way, a nonlinear and non-convex optimal control problem is converted to an equivalent optimal control problem with linear and convex structure, which allows us to obtain an equivalent convex formulation of the problem. So we obtain an approximation of the unknown function by using the Lagrange interpolation, and an approximation of the integral term by using the trapezoidal method. Finally, we solve the problem... 

Recently, Luc defined a dual program for a multiple objective linear program. The dual problem is also a multiple objective linear problem and the weak duality and strong duality theorems for these primal and dual problems have been established.Here, we use these results to establish some relationships between multiple objective linear primal and dual problems. We extend the available results on single objective linear primal and dual problems to multiple objective linear primal and dual problems. Complementary slackness conditions for efficient solutions, and conditions for the existence of weakly efficient solution sets and existence of strictly primal and dual feasible points are... 

In this thesis, we want to present methods that are able to solve the assignment tasks problem in a heterogeneous computing system. These methods are two hybrid methods that are constructed by composing Hopefield Neural Networks with Genetic Algorithms and the Simulated Annealing. First, we solve the relaxed problem by applying Genetic Algorithms and the Simulated Annealing and we compare the results of these ways with other traditional methods. Then, we solve the constrained problem with mentioned hybrid methods. The definition of the problem is as following: Consider a distributed computing system which is comprised of set of processors with different speeds but the same structure. We want...