A globally convergent version of the method of 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.

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A globally convergent method of moving asymptotes with trust region technique

Optimization Methods and Software ◽

10.1080/1055678031000118491 ◽

2003 ◽

Vol 18 (3) ◽

pp. 283-297 ◽

Cited By ~ 9

Author(s):

Qin Ni

Keyword(s):

Trust Region ◽

Method Of Moving Asymptotes ◽

Globally Convergent ◽

Convergent Method ◽

Moving Asymptotes

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A globally convergent modified version of the method of moving asymptotes

Applicable Analysis and Discrete Mathematics ◽

10.2298/aadm181204042g ◽

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.

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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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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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