Sharif Digital Repository

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... 

We explain a new trust-region method for solving unconstrained optimization problems recently introduced in the literature, where the radius update is computed using the information at the current iterate rather than at the preceeding one. The update is then performed according to how well the current model retrospectively predicts the value of the objective function at the last iterate. Global convergence to first- and second-order critical ponits is proved under classical assumptions. Preliminary numerical expriments on CUTEr problems with MATLAB7.7 indicate that the new method is very competitive  

We discuss conjugate gradient methods for which both the gradient and func-tion values are considered in computing the conjugate gradient parameter. We pro-pose new conjugate gradient methods as members of Dai-Liao’s family of conjugate gradient methods and Andrei’s family of hybrid conjugate gradient methods. For computing the conjugate gradient parameter in our methods, three modified secant equations proposed by Zhang, Deng and Chen, Li and Fukushima, and Yuan are used. It is shown that under proper conditions, three of the proposed methods are globally convergent for uniformly convex functions and two other methods are glob-ally convergent for general functions. It is also shown that... 

We describe an interior method for solving bound-constrained systems of equations , recently introduced by S. Bellavia, M. Macconi and B. Morini in the literature. The method makes use of ideas from the classical trust-region Newton method for unconstrained nonlinear equations and the recent interior affine scaling approach for constrained optimization problems. The iterates are generated to be feasible and the bounds are handled implicitly. The method reduces to a standard trust-region method for unconstrained problems when there are no upper or lower bounds on the variables. Global and local fast convergence properties are ... 

We study the general nonlinear integer programming problem. We consider two general classes of this problem: nonlinear integer programming problem and mixed integer nonlinear programming problem (MINLP). We explain the basic concepts for solving these problems and describe common methods for solving them, including branch and bound, Benders decomposition and outer approximation. Furthermore, we introduce two methods based on using penalty methods. Penalty based methods, by using appropriate penalty functions, convert a general nonlinear integer programming problem into a sequence of nonlinear programming problems and these problems are solved by a global optimization algorithm. Computational... 

Considering the special importance of network flow problems in human life, as well as the complexity of solving these problems in very large scales, there are numerous methods to solve them and the interior point methods are the most important approaches among them. In a number of methods, a preconditioned conjugate gradient solver has been applied for the solution of the Karush-Kuhn-Tucker (KKT) system, in each interior point iteration; therefore, the selection of an appropriate preconditioner is a special issue. In spite of presenting different preconditioners in recent years, discussion and implementation of a particular class of triangulated graph-based preconditioners is our main... 

Conjugate gradient methods are useful for large scale nonlinear optimization problem, because they avoid the storage of any matrices. In this thesis, we have investigated an accelerated hybrid conjugate gradient algorithm, recently proposed in the literature. The combining parameter is calculated so that the corresponding direction to the conjugate gradient algorithm, while satisfies the modified secant condition, is a Newton direction. It is shown that for uniformly convex functions and for general nonlinear functions the algorithm with strong Wolfe line search is globally convergent. The algorithm uses an accelerated approach for the reduction of the objective function values by modifying... 

This paper is concerned with the development, numerical implementation, and testing of an algorithm for solving constrained nonlinear least squares problems.The approach is based on the adaptive structured scheme of the exact penalty mehods first Proposed by Mahdavi-Amiri and Bartels and later extended by Mahdavi-Amiri and Ansari. The algorithm is an adaptation to the least squares case of an exact penalty method for solving nonlinearly constrained optimization problems due to Coleman and Conn. It also draws upon the methods of Nocedal and Overton for handling quasi-Newton updates of projected Hessian, upon the methods of Dennis, Gay, and Welsch for approaching the structure of nonlinear... 

We explain a new trust region algorithm for solving unconstrained optimization problems where the redius update is computed using the model information at the current iterate rather than at the preceding one, recently proposed by Bastin, Malmedy, Mouffe, Toint and Tomanos. Then we discuss a modification mixing the concepts of nonmonotone trust region, line search and internal doubling. We use line search to finds a point that satisfies the Wolfe conditions. After that, we explain a new trust region algorithm for solving unconstrained optimization problems where simultaneously satisfies the quasi-Newton condition at each iteration and maintains a positive-definite approximation to the Hessian... 

Exact linear search algorithm recently have been proposed in the literature by Byrd, Lopez-Calvaz and Nocedal for solving nonlinear programming problems. Line search algorithms for nonlinear programming problems must include safeguards to have global convergence properties. We explain an exact penalization approach that extends the class of problems that can be solved with line search SQP methods. In the algorithm, the penalty parameter is adjusted at every iteration to ensure sufficient progress in linear feasibilility and to promote acceptance of the step. A trust region is used to assist in the determination of the penalty parameter. It is shown that the algorithm enjoys favorable... 

An interior point method for nonlinear programming problem recently proposed by Waltz, Morales, Nocedal and Orban is described and implemented [2].The steps are computed by line search based on the primal-dual equations, or trust region based on the conjugate gradient iteration. Steps computed by line search are tried first, but if they are determinded to be ineffective, a trust region iteration that guarantees progress toward a stationary point is used. In order to reduce the calculations, here we propose some modifications. The algorithms are implemented and the programs are tested on a variety of problems. Numerical results based on Dolan-More’ confirm the effectiveness of the algorithms  

We present two projected structured algorithms for solving nonlinearly constrained nonlinear least squares problems. The first algorithm makes use of a line search scheme and the second algorithm utilizes a combined trust region-line search scheme. These approaches are based on an adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method of Coleman and Conn for nonlinearly constrained optimization problems. The structured adaptation also makes use of the ideas of Nocedal and Overton for handling quasi-Newton updates of projected structured Hessians and appropriates the structuring scheme of Dennis, Martinez and Tapia. For robustness of the first algorithm, we... 

In this thesis, we exmine a group of optimization methods called trust region methods for solving semidefinite programming problems. Nowadays, many application problems can be cast as semidefinite programming and problems with very large size are encountered every year. So, having a powerful method for solving such problems is very important. Trust region approach present a new scheme for constructing efficient algorithms to solve semidefinite programming problems.When using interior point methods for solving semidefinite programs (SDPs), one needs to solve a system of linear equations at every iteration. For large problems, solving the system of linear equations can be very expensive. In... 

Decision making is the most important and popular aspect of applying mathematical methods in various fields of human activity. Decisions are nearly always made on the basis of information obtained in conditions of uncertainty. In this thesis, the transportation planning decision (TPD) problem is defined with fuzzy parameters. Our purpose is to simultaneously minimize the total production and transportation costs and the total delivery time with reference to budget constraints and available supply, machine capacities at each source, as well as forecast demand and warehouse space constraints at each destination, and achieve an expected efficient solution for the decision maker according to the... 

We study the Personal Research Space (PRS), that is, the collection of documents a researcher gathers for her research project in order to fnd solutions for a common problem in academic research. During the orientation phase, before the academic research team makes fnal decisions on the course of its studies, abrupt change of directions of studies are common. Ideally, documents in this process are arranged in such a way that time spent in a topic saves a good portion of the time required for research studies in another. We propose an optimization model that provides solutions to parallel this ideal arrangement. PRS as an integral part of the global research system, a highly complex and... 

Several types of large-sized 0-1 Knapsack Problems (KPs) may be easily solved, but in such cases most of the computational effort is used for sorting and reduction. To avoid this, it has been suggested to solve the so-called core of the problem, knapsack problem defined on a small subset of the variables. The exact core cannot, however, be identified before KP is solved to optimality and, thus previously available algorithms had to rely on approximate core sizes. Here, we describe an algorithm for KP recently proposed in the litereture, where the enumerated core size is minimal, and the computational effort for sorting and reduction is also limited in accordance with a hierarchy. The...