Abstract

We introduce set-semidefinite optimization as a new field of vector optimization in infinite dimensions covering semidefinite and copositive programming. This unified approach is based on a special ordering cone, the so-called K-semidefinite cone for which properties are given in detail. Optimality conditions in the KKT form and duality results including the linear case are presented for K-semidefinite optimization problems. A penalty approach is developed for the treatment of the special constraint arising in K-semidefinite optimization problems.

Author information

Contact details are reproduced from the original publication and may be historical.

Johannes Jahn

Department Mathematik, Universität Erlangen-Nürnberg, Martensstr. 3, 91058 Erlangen, Germany

jahn@am.uni-erlangen.de

Keywords

  • Vector optimization
  • convex analysis
  • semidefinite programming
  • copositive programming

Mathematics Subject Classification

90C29, 90C48, 90C22, 90C46

Suggested citation

G. Eichfelder, J. Jahn. “Set-Semidefinite Optimization.” Journal of Convex Analysis 15 (2008), No. 4, 767–801.

Copyright Heldermann Verlag 2008