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Optimality conditions for nonconvex semidefinite programming
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-6252-7815
2000 (English)In: Mathematical programming, ISSN 0025-5610, E-ISSN 1436-4646, Vol. 88, no 1, 105-128 p.Article in journal (Refereed) Published
Abstract [en]

This paper concerns nonlinear semidefinite programming problems for which no convexity assumptions can be made. We derive first- and second-order optimality conditions analogous to those for nonlinear programming. Using techniques similar to those used in nonlinear programming, we extend existing theory to cover situations where the constraint matrix is structurally sparse. The discussion covers the case when strict complementarity does not hold. The regularity conditions used are consistent with those of nonlinear programming in the sense that the conventional optimality conditions for nonlinear programming are obtained when the constraint matrix is diagonal.

Place, publisher, year, edition, pages
2000. Vol. 88, no 1, 105-128 p.
Keyword [en]
semidefinite programming, constrained minimization, optimality, conditions, interior methods, interior-point methods, optimization, complementarity, constraints
URN: urn:nbn:se:kth:diva-19865ISI: 000087947800006OAI: diva2:338557
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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