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projected-gradient-methods
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A Filter-Trust-Region Method for Simple-Bound Constrained Optimization
, M.Sc. Thesis Sharif University of Technology ; Mahdavi Amiri, Nezameddin (Supervisor)
Abstract
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
Energy management through topology optimization of composites microstructure using projected gradient method
, Article Structural and Multidisciplinary Optimization ; Volume 52, Issue 6 , December , 2015 , Pages 1121-1133 ; 1615147X (ISSN) ; Tavakoli, R ; Bagheri, R ; Sharif University of Technology
Springer Verlag
2015
Abstract
In this paper the projected gradient method is applied as an effective gradient-based topology optimization algorithm in order to direct energy propagation through the desired region of composites microstructure. Rayleigh Damping model is also used in order to take the effect of internal damping mechanisms into account and thus, to fill in the gap between the designed layouts and those in reality. The success of the proposed algorithm is illustrated through several numerical experiments by revealing a set of various designed optimal layouts besides their corresponding energy distributions
Design and Analysis of Filter Trust-Region Algorithms for Unconstrained and Bound Constrained Optimization
, M.Sc. Thesis Sharif University of Technology ; Mahdavi Amiri, Nezameddin (Supervisor)
Abstract
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...