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On a special nonlinear problem arising in the study of convex SIP problems
Kostyukova O.I.; Tchemisova T.V.; Yermalinskaya S.A.We continue a study of convex problems of Semi-In¯nite Programming (SIP) started in [6, 7]. In the Implicit Optimality Criterion from [6], we formulated the optimality conditions for convex SIP problem in terms of such the conditions for a special Nonlinear Programming (NLP) problem. In the present paper, we study some speci¯c properties of this nonlinear problem and obtain e±cient optimality conditions for it....
Convex semi-infinite programming: implicit optimality criterion based on the co...
Kostyukova O.I.; Tchemisova T.V.; Yermalinskaya S.A.The paper deals with convex Semi-In¯nite Programming (SIP) problems. A new concept of immobility order is introduced and an algorithm of determination of the immobility orders (DIO algorithm) and so called immobile points is suggested. It is shown that in the presence of the immobile points SIP problems do not satisfy the Slater condition. Given convex SIP problem, we determine all its immobile points and use t...
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