A Sequential Convex Semidefinite Programming Algorithm for Multiple-Load Free Material Optimization

Michael Stingl(stinglam.uni-erlangen.de)
Michal Kocvara(kocvarapenopt.com)
Guenter Leugering(leugeringam.uni-erlangen.de)

Abstract: A new method for the efficient solution of free material optimization problems is introduced. The method extends the sequential convex programming (SCP) concept to a class of optimization problems with matrix variables. The basic idea of the new method is to approximate the original optimization problem by a sequence of subproblems, in which nonlinear functions (defined in matrix variables) are approximated by block-separable convex functions. The subproblems are semidefinite programs with a favorable structure, which can be efficiently solved by existing SDP software. The new method is shown to be globally convergent. The article is concluded by a series of numerical experiments demonstrating the effectiveness of the generalized SCP approach.

Keywords: semidefinite programming, sequential convex programming, material optimization

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Applications -- Science and Engineering (Mechanical Engineering )

Category 3: Applications -- Science and Engineering (Multidisciplinary Design Optimization )

Citation: Preprint 317, Institute of Applied Mathematics, University of Erlangen-Nuremberg, 2007

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Entry Submitted: 09/11/2007
Entry Accepted: 09/11/2007
Entry Last Modified: 09/11/2007

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