Sharif Digital Repository

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... 

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... 

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... 

In this thesis, we propose a first-order interior-point method for linearly constrained smooth optimization which was recently proposed in the literatuare that unifies and extends first-order affine-scaling method and replicator dynamics method for standard quadratic programming. Global convergence and, in the case of quadratic program, the (sub)linear convergence rate and iterate convergence results are derived.The method is implemented and numerical experiments on simplex onstrained problems with 1000 variables is reported  

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  

Robust model predictive control(RMPC) is a control strategy that has been widely adopted in industry and academic researches.In this project we have modified robust nonlinear model predictive control using SOS and dynamic feedback. In this control strategy we will linearize the nonlinear model of the system about it’s operating point. We will consider the error of linearization as an uncertainty and find an upper bound for uncertainty. Then we will change control objective to minimizing this upper bound. The most advantage of changing the control objective is that nonlinear system results a non-convex optimization problem but this strategy terminates a convex optimization problem. To find... 

Turbulence can distort and corrupt the image in quite a few ways when light from a distance star or another astronomical object enters the Earth's atmosphere. It is inevitable that all images produced by any telescope on ther Earth are blurred by these distortions. Adaptive Optics is a technology used to improve the performance of optical systems by reducing the effect of wavefront distortions: it aims at correcting the deformations of an incoming wavefront by deforming a mirror in order to compensate for the distortion. The research work reported in this thesis presents a solution to the surface shape control problems in a Deformable Mirror system. Our first goal is to derive equations that... 

Path planning of a robot inside an environment with obstacles is to determine an appropriate path for moving from an initial point to a destination without colliding the obstacles. The main considerations in selecting such a path are its length and simplicity in terms of links or turn angles. In this paper, we study this problem for a point robot in the plane and our goal is to minimize the path length. We solve this problem by converting it to an optimization problem and solving the resulted optimization problem by a recurrent neural network. According to the implementation results, the obtained path is a proper approximation of the minimum length path, especially when obstacles are not too... 

We explain a new penalty method recently introduced in the literature for solv-ing constrained optimization problems. In this method, the penalty parameter is adjusted dynamically at every iteration to ensure su?cient progress in linear feasi-bility. A trust region is used to assist in the determination of the penalty parameter, but not in the step computation. It is shown that the algorithm has global conver-gence. We implement the algorithm and test the program on a number of di?cult optimization problems. The numerical results con?rm the e?ectiveness of the algo-rithm  

There are many limitations to determine relationships within biological systems. Among the limitations of these systems, one can consider the lack of sufficient information about them, such as the complete knowledge of many networks, the lack of reaction information, the complexity of the analysis of these reactions, etc. One of the methods to analyze these systems is called flux balance analysis. This method consists of three parts: objective function, equal constraints and unequal constraints. Among the features available in this method, we can mention less need for experimental information and no need for high processing systems. In order to determine the objective functions in this...