Optimality conditions for nonconvex semidefinite programming

Authors
Citation
A. Forsgren, Optimality conditions for nonconvex semidefinite programming, MATH PROGR, 88(1), 2000, pp. 105-128
Citations number
25
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL PROGRAMMING
ISSN journal
0025-5610 → ACNP
Volume
88
Issue
1
Year of publication
2000
Pages
105 - 128
Database
ISI
SICI code
0025-5610(200006)88:1<105:OCFNSP>2.0.ZU;2-E
Abstract
This paper concerns nonlinear semidefinite programming problems for which n o convexity assumptions can be made. We derive first- and second-order opti mality conditions analogous to those for nonlinear programming. Using techn iques similar to those used in nonlinear programming, we extend existing th eory 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 prog ramming in the sense that the conventional optimality conditions for nonlin ear programming are obtained when the constraint matrix is diagonal.