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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
Graph-Based Preconditioners for Network Flow Problems
, M.Sc. Thesis Sharif University of Technology ; Mahdavi Amiri, Nezamoddin (Supervisor)
Abstract
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...
An Implementation of an Interior Point Algorithm for Nonlinear Optimization Combining line Search and Trust Region Steps
, M.Sc. Thesis Sharif University of Technology ; Mahdavi-Amiri, Nezamoddin (Supervisor)
Abstract
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
Implementation of New Hybrid Conjugate Gradient Algorithms
Based on Modified BFGS Updates
,
M.Sc. Thesis
Sharif University of Technology
;
Mahdavi-Amiri, Nezam
(Supervisor)
Abstract
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...
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...
Iteratively Constructing Preconditioners via the Conjugate Gradient Method
, M.Sc. Thesis Sharif University of Technology ; Farhadi, Hamid Reza (Supervisor)
Abstract
The main goal of this work is solving system of linear equations Ax = b, where A is a n_n square matrix, b is a n_1 vector and x is the vector of unknowns. When n is large, using direct methods is not economical. Thus, the system is solved by iterative methods. At first, projection method onto subspace K _ Rn with dimension m _ n is described, and then this subspace K is equalized with the krylov subspace. Then,some samples of projection methods onto the krylov subspace, such as FOM, GMRES and CG (Conjugate Gradient), are considered. The preconditioning of the linear system is explained, that is, instead of solving system Ax = b, the system PAx = Pb (P nonsingular), is solved, such that the...
Conjugate Residual Method for Large Scale Unconstrained Nonlinear Optimization
, M.Sc. Thesis Sharif University of Technology ; Mahdavi Amiri, Nezam (Supervisor)
Abstract
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...
New Conjugate Gradient Methods for Unconstrained Optimization
, Ph.D. Dissertation Sharif University of Technology ; Mahdavi Amiri, Nezamoddin (Supervisor)
Abstract
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...
Properties and Numerical Performance of Nonlinear Conjugate Gradient Methods Whit Modified Secant Equations and New Conjugacy Conditions
, M.Sc. Thesis Sharif University of Technology ; Mahdavi Amiri, Nezamedin (Supervisor)
Abstract
Conjugate gradient methods are appealing for large scale nonlinear optimization problems, because they avoid the storage of matrices. Recently, a new conjugacy condition proposed by Dai and Liao, considers an inexact line search scheme that reduces to the old one if the line search is exact. Based on this condition, a new conjugate gradient method was proposed that has fast convergence. Later, Yabe and Takano, based on new conjugacy condition and modified secant condition, proposed another conjugate gradient method. This method takes both the available gradient and function value information and achieves a high-order accuracy in approximating the second-order curvature of the objective...
Solving a Smooth Approximation of the Sparse Recovery Problem Using the Three-Term Conjugate Gradient Algorithms
, M.Sc. Thesis Sharif University of Technology ; Mahdavi Amiri, Nezamoddin (Supervisor)
Abstract
Line search-based methods are known as a category of the most efficient iterative algo- rithms for solving unconstrained optimization problems. Among them, the conjugate gradient method is of particular importance in solving large-scale contemporary world problems due to its simplicity of structure, low memory requirement and strong convergence characteristics. In spite of the desirable numerical behavior of the conjugate gradient method, this method generally lacks the descent property even for uniformly convex objective functions. To overcome this defect, some effective modifications have been presented in the literature. Amidst, the three-term extension attracted the attention of many...
Solving of Nonconvex Optimization Problem Using Trust-Region Newton-Conjugate Gradient Method with Strong Second-Order Complexity Guarantees
, M.Sc. Thesis Sharif University of Technology ; Mahdavi Amiri, Nezamoddin (Supervisor)
Abstract
Worst-case complexity guarantees for non-convex optimization algorithms is a topic that have received increasing attention. Here , we review trust-region Newton methods recently proposed in the literature . After a slight modification of the main model , two methods are proposed : one of them is based on the exact solution of the sub-problem , and the other is based on the inexact solution of the sub-problem , such as ``trust-region Newton-conjugate gradient " method with the complexity bounds corresponding to the best known bounds for this class of algorithms . We implement the proposed algorithms and test the programs in the Python software environment
Implicit Solution of 2-dimensional Compressible Flow, Using Parallel Krylov Method
,
M.Sc. Thesis
Sharif University of Technology
;
Taeibi Rahni, Mohammad
(Supervisor)
;
Sabetghadam, Fereidoon
(Supervisor)
Abstract
Numerical Simulation of two-dimensional steady compressible fluid flow on unstructured grids was accomplished using a fast implicit algorithm. To solve the copmlete two-dimensional Navier-Stokes equations, implicit time stepping was used which results in a large sparse linear system in each iteration. To solve the linear system, the biconjugate gradient method which belongs to Krylov subspace methods family, with an ILU(0) preconditioner was used. For accelerating the solution in large problems, parallel processing was used for linear system to be solved faster. Two upwind methods, namely Roe’s and AUSM+ methods were used for spatial descritizaion of inviscid fluxes with a MUSCL algorithm...
Correction of Time-Dependent Origin-Destination Demand in Dynamic Traffic Assignment
, M.Sc. Thesis Sharif University of Technology ; Zakaei Ashtiani, Hedayat (Supervisor)
Abstract
Time-dependent origin-destination demand is a key input in dynamic traffic assignment in advanced traffic management systems, and the result of dynamic traffic assignment is dependent on the accuracy of this information. One method to achieve time dependent demand matrices is using a primary demand matrix and volume traffic counts in some links of network. In this thesis a bi-level model is used to correct the demand matrix and the extended gradient method is suggested to solve the problem. The extended gradient is an iterative method that in each iteration, corrects the demand matrix in a way that the estimated traffic flow be close to the observed traffic flow. Execution of this method in...
Accelerated Hybrid Conjugate Gradient Algorithm with Modified Secant Condition
, M.Sc. Thesis Sharif University of Technology ; Mahdavi Amiri, Nezamoddin (Supervisor)
Abstract
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...
Two new conjugate gradient methods based on modified secant equations
, Article Journal of Computational and Applied Mathematics ; Volume 234, Issue 5 , 2010 , Pages 1374-1386 ; 03770427 (ISSN) ; Ghanbari, R ; Mahdavi Amiri, N ; Sharif University of Technology
2010
Abstract
Following the approach proposed by Dai and Liao, we introduce two nonlinear conjugate gradient methods for unconstrained optimization problems. One of our proposed methods is based on a modified version of the secant equation proposed by Zhang, Deng and Chen, and Zhang and Xu, and the other is based on the modified BFGS update proposed by Yuan. An interesting feature of our methods is their account of both the gradient and function values. Under proper conditions, we show that one of the proposed methods is globally convergent for general functions and that the other is globally convergent for uniformly convex functions. To enhance the performance of the line search procedure, we also...
Two modified hybrid conjugate gradient methods based on a hybrid secant equation
, Article Mathematical Modelling and Analysis ; Volume 18, Issue 1 , 2013 , Pages 32-52 ; 13926292 (ISSN) ; Mahdavi Amiri, N ; Sharif University of Technology
2013
Abstract
Taking advantage of the attractive features of Hestenes-Stiefel and Dai-Yuan conjugate gradient methods, we suggest two globally convergent hybridizations of these methods following Andrei's approach of hybridizing the conjugate gradient parameters convexly and Powell's approach of nonnegative restriction of the conjugate gradient parameters. In our methods, the hybridization parameter is obtained based on a recently proposed hybrid secant equation. Numerical results demonstrating the efficiency of the proposed methods are reported
Time-varying dual accelerated gradient ascent: A fast network optimization algorithm
, Article Journal of Parallel and Distributed Computing ; Volume 165 , 2022 , Pages 130-141 ; 07437315 (ISSN) ; Mahdavi Amiri, N ; Sharif University of Technology
Academic Press Inc
2022
Abstract
We propose a time-varying dual accelerated gradient method for minimizing the average of n strongly convex and smooth functions over a time-varying network with n nodes. We prove that the time-varying dual accelerated gradient ascent method converges at an R-linear rate with the time to reach an ϵ-neighborhood of the solution being of O([Formula presented]ln[Formula presented]), where c is a constant depending on the graph and objective function parameters and M is a constant depending on the initial values. We test the proposed method on two classes of problems: L2-regularized least squares and logistic classification problems. For each class, we generate 1000 problems and use the...
The strain gradient approach for determination of forming limit stress and strain diagrams
, Article Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture ; Volume 222, Issue 4 , 2008 , Pages 467-483 ; 09544054 (ISSN) ; Hashemi, R ; Assempour, A ; Sharif University of Technology
2008
Abstract
The forming limit stress diagram (FLSD) has been reported as being much less path dependent and much more favourable than the forming limit diagram (FLD) in representing forming limits in the numerical simulation of sheet metal forming processes. Therefore, the purpose of this study was to develop a methodology for the prediction of the forming limits both in strain and stress forms. All simulations are based on strain gradient theory of plasticity in conjunction with the Marciniak-Kuczynski (M-K) approach. This approach introduces an internal length scale into conventional constitutive equations and takes into account the effects of deformation inhomogeneity and material softening. The...
Structured multiblock body-fitted grids solution of transient inverse heat conduction problems in an arbitrary geometry
, Article Numerical Heat Transfer, Part B: Fundamentals ; Volume 54, Issue 3 , July , 2008 , Pages 260-290 ; 10407790 (ISSN) ; Kazemzadeh Hannani, S ; Farhanieh, B ; Sharif University of Technology
2008
Abstract
The aim of this study is to develop iterative regularization algorithms based on parameter and function estimation techniques to solve two-dimensional/axisymmetric transient inverse heat conduction problems in curvilinear coordinate system. The multiblock method is used for geometric decomposition of the physical domain into regions with patched-overlapped interface grids. The central finite-difference version of the alternating-direction implicit technique together with structured body-fitted grids is implemented for numerical solution of the direct problem and other partial differential equations derived by inverse analysis. The approach of estimating unknown parameters and functions is...
Robust adaptive fractional order proportional integral derivative controller design for uncertain fractional order nonlinear systems using sliding mode control
, Article Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering ; Volume 232, Issue 5 , 1 May , 2018 , Pages 550-557 ; 09596518 (ISSN) ; Salarieh, H ; Sharif University of Technology
SAGE Publications Ltd
2018
Abstract
This article presents a robust adaptive fractional order proportional integral derivative controller for a class of uncertain fractional order nonlinear systems using fractional order sliding mode control. The goal is to achieve closed-loop control system robustness against the system uncertainty and external disturbance. The fractional order proportional integral derivative controller gains are adjustable and will be updated using the gradient method from a proper sliding surface. A supervisory controller is used to guarantee the stability of the closed-loop fractional order proportional integral derivative control system. Finally, fractional order Duffing–Holmes system is used to verify...