Optimality conditions for nonconvex semidefinite programming

Optimality conditions for nonconvex semidefinite programming

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Article ID: iaor20013580
Country: Germany
Volume: 88
Issue: 1
Start Page Number: 105
End Page Number: 128
Publication Date: Jan 2000
Journal: Mathematical Programming
Authors:
Keywords: semidefinite programming
Abstract:

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.

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