scholarly journals A globally convergent modified multivariate version of the method of moving asymptotes

2021 ◽  
pp. 33-33
Author(s):  
Allal Guessab ◽  
Abderrazak Driouch
Keyword(s):  
Present Method ◽  
New Method ◽  
Method Of Moving Asymptotes ◽  
Globally Convergent ◽  
Moving Asymptotes

In this paper, we introduce an extension of our previous paper, A globally convergent version to the Method of Moving Asymptotes, in a multivariate setting. The proposed multivariate version is a globally convergent result for a new method, which consists iteratively of the solution of a modified version of the method of moving asymptotes. It is shown that the algorithm generated has some desirable properties. We state the conditions under which the present method is guaranteed to converge geometrically. The resulting algorithms are tested numerically and compared with several well-known methods.

scholarly journals A globally convergent modified version of the method of moving asymptotes

2020 ◽  
pp. 41-41
Author(s):  
Allal Guessab ◽  
Abderrazak Driouch ◽  
Otheman Nouisser
Keyword(s):  
Iterative Process ◽  
Present Method ◽  
Experimental Results ◽  
Order Information ◽  
Bfgs Method ◽  
Strictly Convex ◽  
Method Of Moving Asymptotes ◽  
Globally Convergent ◽  
Geometrical Convergence ◽  
Moving Asymptotes

A new modified moving asymptotes method is presented. In each step of the iterative process, a strictly convex approximating subproblem is generated and explicitly solved. In doing so we propose a strategy to incorporate a modified second-order information for the moving asymptotes location. Under natural assumptions, we prove the geometrical convergence. In addition the experimental results reveal that the present method is significantly faster compared to the [1] method, Newton's method and the BFGS Method.

scholarly journals A globally convergent modified version of the method of moving asymptotes

2019 ◽  
Vol 13 (3) ◽  
pp. 905-917
Author(s):  
Allal Guessab ◽  
Abderrazak Driouch ◽  
Otheman Nouisser
Keyword(s):  
Iterative Process ◽  
Present Method ◽  
Experimental Results ◽  
Order Information ◽  
Bfgs Method ◽  
Strictly Convex ◽  
Method Of Moving Asymptotes ◽  
Globally Convergent ◽  
Geometrical Convergence ◽  
Moving Asymptotes

A new modified moving asymptotes method is presented. In each step of the iterative process, a strictly convex approximating subproblem is generated and explicitly solved. In doing so we propose a strategy to incorporate a modified second-order information for the moving asymptotes location. Under natural assumptions, we prove the geometrical convergence. In addition the experimental results reveal that the present method is significantly faster compared to the [1] method, Newton's method and the BFGS Method.

A CONVEX APPROXIMATION METHOD FOR LARGE SCALE LINEAR INEQUALITY CONSTRAINED MINIMIZATION

2010 ◽  
Vol 27 (01) ◽  
pp. 85-101
Author(s):  
HAI-JUN WANG ◽  
QIN NI
Keyword(s):  
Large Scale ◽  
Linear Inequality ◽  
Trust Region ◽  
Inequality Constraints ◽  
New Method ◽  
Approximation Properties ◽  
Linear Inequality Constraints ◽  
Method Of Moving Asymptotes ◽  
Large Scale Problems ◽  
Moving Asymptotes

A new method of moving asymptotes for large scale minimization subject to linear inequality constraints is discussed in this paper. In each step of the iterative process, a descend direction is obtained by solving a convex separable subproblem with dual technique. The new rules for controlling the asymptotes parameters are designed by the trust region radius and some approximation properties such that the global convergence of the new method are obtained. The numerical results show that the new method may be capable of processing some large scale problems.

A Penalty-Free Method with Trust Region for Nonlinear Semidefinite Programming

2015 ◽  
Vol 32 (01) ◽  
pp. 1540006 ◽  
Author(s):  
Zhongwen Chen ◽  
Shicai Miao
Keyword(s):  
Semidefinite Programming ◽  
Objective Function ◽  
Penalty Function ◽  
Trust Region ◽  
Numerical Results ◽  
New Method ◽  
Penalty Parameter ◽  
Nonlinear Semidefinite Programming ◽  
Globally Convergent ◽  
Nonlinear Objective Function

In this paper, we propose a class of new penalty-free method, which does not use any penalty function or a filter, to solve nonlinear semidefinite programming (NSDP). So the choice of the penalty parameter and the storage of filter set are avoided. The new method adopts trust region framework to compute a trial step. The trial step is then either accepted or rejected based on the some acceptable criteria which depends on reductions attained in the nonlinear objective function and in the measure of constraint infeasibility. Under the suitable assumptions, we prove that the algorithm is well defined and globally convergent. Finally, the preliminary numerical results are reported.

Topology Synthesis of Large-Displacement Compliant Mechanisms

1999 ◽  
Author(s):  
Claus B. W. Pedersen ◽  
Thomas Buhl ◽  
Ole Sigmund
Keyword(s):  
Sensitivity Analysis ◽  
Optimization Problem ◽  
Adjoint Method ◽  
Compliant Mechanisms ◽  
Large Displacement ◽  
Element Formulation ◽  
Method Of Moving Asymptotes ◽  
Synthesis Tool ◽  
Lagrangian Finite Element ◽  
Moving Asymptotes

Abstract This paper describes the use of topology optimization as a synthesis tool for the design of large-displacement compliant mechanisms. An objective function for the synthesis of large-displacement mechanisms is proposed together with a formulation for synthesis of path-generating compliant mechanisms. The responses of the compliant mechanisms are modelled using a Total Lagrangian finite element formulation, the sensitivity analysis is performed using the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. Procedures to circumvent some numerical problems are discussed.

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