Journal of Convex Analysis 15 (2008), No. 4, 767--801
Copyright Heldermann Verlag 2008
Set-Semidefinite Optimization
Gabriele Eichfelder
Department Mathematik, Universität Erlangen-Nürnberg, Martensstr. 3, 91058 Erlangen, Germany
Gabriele.Eichfelder@am.uni-erlangen.de
Johannes Jahn
Department Mathematik, Universität Erlangen-Nürnberg, Martensstr. 3, 91058 Erlangen, Germany
jahn@am.uni-erlangen.de
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.
Keywords: Vector optimization, convex analysis, semidefinite programming, copositive programming.
MSC: 90C29, 90C48, 90C22, 90C46
[ Fulltext-pdf (261 KB)] for subscribers only.