The method of moving asymptotes—a new method for structural optimization

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.

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

Applicable Analysis and Discrete Mathematics ◽

10.2298/aadm190325033g ◽

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.

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A new method of moving asymptotes for large-scale unconstrained optimization

Applied Mathematics and Computation ◽

10.1016/j.amc.2008.03.035 ◽

2008 ◽

Vol 203 (1) ◽

pp. 62-71 ◽

Cited By ~ 6

Author(s):

Haijun Wang ◽

Qin Ni

Keyword(s):

Unconstrained Optimization ◽

Large Scale ◽

New Method ◽

Method Of Moving Asymptotes ◽

Large Scale Unconstrained Optimization ◽

Moving Asymptotes

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Topology Synthesis of Large-Displacement Compliant Mechanisms

Volume 1: 25th Design Automation Conference ◽

10.1115/detc99/dac-8554 ◽

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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