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First-Order Optimality Conditions for Nonsmooth Semidefinite Programming
Author(s): 
Pages: 1-9
Year: Issue:  3
Journal: OPERATIONS RESEARCH TRANSACTIONS

Keyword:  Operation researchsemidefinite programmingnonsmooth analysisoptimality conditions;
Abstract: This paper concerns nonsmooth semidefinite programming problems. We derive first-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. This discussion covers the case when strict complementarity dose 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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