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A constructive algorithm for determination of immobile indices in convex SIP pr...
Kostyukova, O. I.; Tchemisova, T. V.We consider convex Semi-Infinite Programming (SIP) problems with polyhedral index sets. For these problems, we generalize the concepts of immobile indices and their immobility orders (that are objective and important characteristics of the feasible sets permitting to formulate new efficient optimality conditions. We describe and justify a finite constructive algorithm (DIIPS algorithm) that determines im...
Implicit optimality criterion for convex SIP problem with box constrained index...
Kostyukova, O.I.; Tchemisova, T.V.We consider a convex problem of Semi-Infinite Programming (SIP) with multidimensional index set. In study of this problem we apply the approach suggested in [20] for convex SIP problems with one-dimensional index sets and based on the notions of immobile indices and their immobility orders. For the problem under consideration we formulate optimality conditions that are explicit and have the form of criterion. W...
Optimality criteria without constraint qualications for linear semidenite prob...
Kostyukova O.I.; Tchemisova T.V.We consider two closely related optimization problems: a problem of convex Semi- Infinite Programming with multidimensional index set and a linear problem of Semidefinite Programming. In study of these problems we apply the approach suggested in our recent paper [14] and based on the notions of immobile indices and their immobility orders. For the linear semidefinite problem, we define the subspace of immobile ...
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: explicit optimality conditions
Kostyukova O.I.; Tchemisova T.V.We consider the convex Semi-In¯nite Programming (SIP) problem where objec- tive function and constraint function are convex w.r.t. a ¯nite-dimensional variable x and all of these functions are su±ciently smooth in their domains. The constraint function depends also on so called time variable t that is de¯ned on the compact set T ½ R. In our recent paper [15] the new concept of immobility order of the points of ...
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...
Rigidity of abnormal extrema in the problem of non-linear programming with mixe...
Sarychev, A.V.; Tchemisova, T. V.We study abnormal extremum in the problem of non-linear pro- gramming with mixed constraints. Abnormal extremum occurs when in necessary optimality conditions the Lagrange multiplier, which cor- responds to the objective function, vanishes. We demonstrate that in this case abnormal second-order su±cient optimality conditions guar- antee rigidity of the corresponding extremal point, which means iso- latedness of...
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