Sharif Digital Repository

Multi-objective optimization is an important branch of optimization. One of the most common methods to solve multi-objective problems is to find the Pareto efficient points. In practical applications, there are many instances in which there are no analytical formula for the function and only approximate values at some points are available. Derivative-free optimization is one approach to solve these problems.Here, we consider one of the multi-objective derivative-free optimization techniques called direct multisearch (DMS), recently proposed in the literature. In this method, a commonly used single objective optimization method is generalized to the multiobjective case. A popular category of... 

Design, analysis and practical implementation of the filter trust-region algorithms are investigated. First, we introduce two filter trust-region algorithms for solving the unconstrained optimization problem. These algorithms belong to two different class of optimization algorithms: (1) The monotone class, and (2) The non-monotone class. We prove the global convergence of the sequence of the iterates generated by the new algorithms to the first and second order critical points. Then, we propose a filter trust-region algorithm for solving bound constrained optimization problems and show that the algorithm converges to a first order critical point. Moreover, we address some well known... 

We consider sequential quadratic programming (SQP) methods applied to optimization problems with nonlinear equality constraints and simple bounds, recently introduced in the literature. In particular, we describe and analyze a truncated SQP algorithm due to Izmailov and Solodov in which subproblems are solved approximately by an infeasible predictor-corrector interior-point method, followed by setting to zero some variables and some multipliers so that complementarity conditions for approximate solutions are satisfied. Verifiable truncation conditions based on the residual of optimality conditions of subproblems are explained to ensure both global and fast local convergence. Global... 

We are concerned with describing an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained by making a linear approximation to the penalty function inside a trust region. In the second stage, an equality constrained quadratic program (EQP) is solved involving only those constraints that are active at the solution of the linear program. The EQP incorporates a trust-region constraint and is solved (inexactly) by means of a... 

In financial portfolio problem, optimization models with uncertainty has been considered. The multi-stage stochastic programming methodology has been used as a solution method for these problems. In this study, we use multi-stage programming with uncertainity to evaluate the asset allocation problem. Some general models have been introduced for problem solving. Non-anticipativity and parent-child models are implemented and solved by both simplex and interior-point methods and the results are compared. The results show the parent-child model to have a better performance. Also, the interior-point method appears to need less computing time than the simplex method  

Column generation technique has became a very important tool in the solution of linear programming problems. Column generation techniques start with solving a reduced version of the master problem. Recently, variations of the standard column generation approach have been proposed which use interior point of the dual feasible set instead of optimal slutions. So, primal-dual column generation technique uses a primal-dual interior point method to obtain well-centered non-optimal solutions of the restricted master problem. We show that the method converges to an optimal solution of the master problem. Then, an improved primal simplex algorithm (IPS) for degenerate linear problems is proposed.... 

Nonlinear optimization is concerned with finding optimal solutions of optimization problems, where the objective function or some constraints are nonlinear. Since many issues in science and engineering can be expressed and formulated as a nonlinear problem, we investigate BFGS method, a successful iterative quasi-Newton method, for solving non-convex problems in unconstrained optimization. The method is based on the work of Yuan and his colleagues, making use of modified weak Wolfe-Powell line search, introducing a certain condition, introducing the next point if the condition is met, introducing a parabolic function if the condition is not established and obtaining the projection point and... 

Image classification is a crucial problem in machine learning. Discriminative dictionary learning is recognized as a powerful method for image classification. By incorporating various label information in the dictionary learning process, a dictionary can be generated that reconstructs the original data while focusing on discriminative features. Here, previous dictionary learning-based image classification methods are first reviewed, and then a novel approach, called Deep Discriminative Dictionary Pair Learning, which was introduced by Zhou and colleagues, is explained for image classification. Unlike traditional methods, this approach utilizes deep features extracted from autoencoders as... 

In this thesis, arranged by [6], the multiplier method is used to solve the network problems with nonlinear constraints and the Newton-like methods are used for updating the required parameters. This method, recently proposed in the literature, is based on solving a sequence of nonlinear optimization subproblems, dependent on the main problem, such that sequence of solutions of these problems converge to the solution of the main problem. In fact, to obtain an acceptable approximation of the main solution, it is needed to solve just a finite number of nonlinear subproblems. The main idea of the multiplier methods is based on eliminating some constraints and adding a penalty term to the... 

Bezier curves are among important curves which are broadly used in different fields such as computer graphic, vector graphic and animation. Among softwares in which these curves are used nowadays are: Adobe, Inkscape, GIMP, Adobe Photoshop, and Illustrator. An important concept in drawing the Bezier curves is to plot these curveswith fewer numbers of control points (low degree). Many algorithms have been introduced to reduce the degree of bezier curves. Here we first describe Bezier curves and their properties. Our main concern here is implementation of a new algorithm for multi-degree reduction of Bezier curves which are constrainted. The algorithm has recently been proposed byWozny and... 

In the modern world, steganography is an image processing technique, revealing to be a suitable process for information hiding. In most cases, steganography has shown to be more effective than cryptography techniques. Recently, there have been attempts to improve the stego-image quality and hiding capacity by introducing new methods. Here, we inspect the advantages and disadvantages of some new steganography methods for digital images. The implemented methods are color and grayscale image steganography with OPVSP algorithm, BRL and GRL methods, and the simple LSB method with OPAP algorithm. Here, we compare the implementation results of these methods using MATLAB 7.4.0, with other common... 

We explain new interval methods, recently introduced in the literature, for solving unconstrained and constrained global optimization problems. The strategy is characterized by a subdivision of the argument intervals of the expression and a recomputation of the expression with these new intervals. By varying the selection and termination criteria, we explain new variants. These methods are used to solve problems with an objective function that has possibly a large number of local minima and constraints that may be nonlinear or nonconvex. We describe algorithms that return global minima and points at which the objective function is within a defined distance from the global minima. Numerical... 

We explain a filter-trust-region algorithm for solving nonlinear optimization problems with simple bounds recently proposed by Sainvitu and Toint. The algorithm is shown to be globally convergent to at least one first-order critical point. We implement the algorithm and test the program on various problems. The results show the effectiveness of the algorithm  

The Wedderburn rank reduction formula and the ABS algorithms are powerful methods for developing matrix factorizations and many fundamental numerical linear algebra processes such as Gramm- Schmidt, conjugate direction and Lanczos methods. Esmaeili, Mahdavi-Amiri and Spedicato introduced a class of integer ABS algorithms for solving linear systems of Diophantine equations. In a recent work, Khorramizadeh and Mahdavi-Amiri have also presented a new class of extended integer ABS algorithms for solving linear Diophantine systems by computing an integer basis for the null space while controlling the growth of intermediate results. Here, we propose new approches to develop a new class of extended... 

Motivated by the Karush-Kuhn-Tucker optimality conditions for a sort of quadratic programs, we first discuss a class of nonlinear complementarity problems (NCPs). Then, we explain a kind of inverse problems of the NCP for a given feasible decision , and we characterize the set of parameter values for which there exists a point such that ( , ) forms a solution of the NCP and require the parameter values to be adjusted as little as possible. This leads to an inverse optimization problem. In particular, under , and Frobenius norms as well as affine maps, we discuss three simple and efficient solution methods recently introduced in the literature, for the inverse NCPs. Finally, some... 

Ant algorithms are optimization algorithms inspired by natural behavior of real ants, which can find the shortest path between nest and food. These algorithms are used to solve numerous complex optimization and combinatorial problems. In recent years, ant algorithms have been used in image processing, specially in edge detection. Edge detection being important and having applications in image processing, several edge detection algorithms have been presented. Our goal is to study edge detection processes based on ant algorithms. Four algorithms recently proposed in the literature are implemented, and the results presented by their authors are verified. Furthermore, implemented algorithms are... 

Minimizing problems with either orthogonal or spherical constraints has a great number of applications in combinatorial optimization, polynomial optimization,eigenvalue problem, estimation to the nearest correlation between matrices of low rank, etc. Solving this kind of problem is hard, because feasible spaces for constraints are non-convex, and solving them is very costly as well. For confronting with this issue, The Cayley transform is used for keeping constraints,and, based on this technique, a smooth curve algorithm with low flop is compared with some algorithms based on is projections and geodesics . Efficiency of the algorithm, recently in introduced the literature, is proved on a... 

Image processing is very important in several applications. Here we use a rectangular grid for image processing. Other approaches exist in the literature. One new approach is to change the grid from rectangular to hexagonal, due to its various advantages over the latter. Main advantage of the hexagonal structure in image processing is its resemblance with the arrangement of photoreceptors in the human eyes. The change in arrangement amounts to requiring less pixels. There is no inconsistency in pixel connectivity and thus angular resolution is higher in this arrangement. Our goal here is to study lossless compression algorithms for images with hexagonal pixels. First, we consider the... 

Support vector regression (SVR) in the field of machine learning attracted much attention because of its attractive features and high efficiency for high-dimensional and nonlinear data. Although support vector regression has shown to be very effective for prediction problems, it is necessary to adjust the parameters contained therein to obtain the desired output with error rates. In the past, this was done manually, by trial and error. Over time and by development of optimization algorithms, one of the newest methods to solve such problems is the meta-heuristic optimization algorithms. Therefore, in this thesis, we use the firefly optimization algorithm, which is a population-based... 

Two algorithms for solving constrained nonlinear programming problems (NLPs) are proposed. The first algorithm is an inexact nonmonotone filter sequential quadratic programming iNFSQP method. In each iteration of the algorithm, the search direction is computed using an inexact solution of a strictly convex quadratic program (QP). The search direction is a descent direction for the objective function (in feasible iterations) or a descent direction for the constraints violation function (in infeasible iterations). In this algorithm, the penalty parameter is updated in such a way that the search direction is a descent direction for the penalty function, which is a combination of the objective...