Publicación: A COMPLETE CHARACTERIZATION OF STRONG DUALITY IN NONCONVEX OPTIMIZATION WITH A SINGLE CONSTRAINT
Fecha
2012
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JOURNAL OF GLOBAL OPTIMIZATION
Resumen
WE FIRST ESTABLISH SUFFICIENT CONDITIONS ENSURING STRONG DUALITY FOR CONE CONSTRAINED NONCONVEX OPTIMIZATION PROBLEMS UNDER A GENERALIZED SLATER-TYPE CONDITION. SUCH CONDITIONS ALLOW US TO COVER SITUATIONS WHERE RECENT RESULTS CANNOT BE APPLIED. AFTERWARDS, WE PROVIDE A NEW COMPLETE CHARACTERIZATION OF STRONG DUALITY FOR A PROBLEM WITH A SINGLE CONSTRAINT: SHOWING, IN PARTICULAR, THAT STRONG DUALITY STILL HOLDS WITHOUT THE STANDARD SLATER CONDITION. THIS YIELDS LAGRANGE MULTIPLIERS CHARACTERIZATIONS OF GLOBAL OPTIMALITY IN CASE OF (NOT NECESSARILY CONVEX) QUADRATIC HOMOGENEOUS FUNCTIONS AFTER APPLYING A GENERALIZED JOINT-RANGE CONVEXITY RESULT. FURTHERMORE, A RESULT WHICH REDUCES A CONSTRAINED MINIMIZATION PROBLEM INTO ONE WITH A SINGLE CONSTRAINT UNDER GENERALIZED CONVEXITY ASSUMPTIONS, IS ALSO PRESENTED.
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STRONG DUALITY, NONCONVEX OPTIMIZATION
