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A New Non-linear Semidefinite Programming Algorithm with an Application to Multidisciplinary Free Material Optimization

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Optimal Control of Coupled Systems of Partial Differential Equations

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 158))

Abstract

A new method and algorithm for the efficient solution of a class of nonlinear semidefinite programming problems is introduced. The new method extends a concept proposed recently for the solution of convex semidefinite programs based on the sequential convex programming (SCP) idea. In the core of the method, a generally non-convex semidefinite program is replaced by a sequence of subproblems, in which nonlinear constraint and objective functions defined in matrix variables are approximated by block separable convex models. Global convergence is proved under reasonable assumptions. The article is concluded by numerical experiments with challenging Free Material Optimization problems subject to displacement constraints.

This work has been partially supported by the EU Commission in the Sixth Framework Program, Project No. 30717 PLATO-N.

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Author information

Authors and Affiliations

  1. Applied Mathematics II, Department of Mathematics, University of Erlangen, Martensstr. 3, D-91058, Erlangen, Germany

    M. Stingl & G. Leugering

  2. School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK

    M. Kočvara

Authors
  1. M. Stingl
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  2. M. Kočvara
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  3. G. Leugering
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Editor information

Editors and Affiliations

  1. Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Heinrichstrasse 36, 8010, Graz, Austria

    Karl Kunisch

  2. Abt. Partielle Differentialgleichung Weierstraß-Institut für Angewandte Analysis und Stochastik, Humboldt-Universität zu Berlin, Mohrenstrasse 39, 10117, Berlin, Germany

    Jürgen Sprekels

  3. LS Angewandte Mathematik II Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, Martensstrasse 3, 91058, Erlangen, Germany

    Günter Leugering

  4. Institut für Mathematik Fak. II Mathematik & Naturwissenschaften, TU Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Fredi Tröltzsch

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Stingl, M., Kočvara, M., Leugering, G. (2009). A New Non-linear Semidefinite Programming Algorithm with an Application to Multidisciplinary Free Material Optimization. In: Kunisch, K., Sprekels, J., Leugering, G., Tröltzsch, F. (eds) Optimal Control of Coupled Systems of Partial Differential Equations. International Series of Numerical Mathematics, vol 158. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-8923-9_16

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