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Titlebook: Optimality and Stability in Mathematical Programming; Monique Guignard Book 1982Latest edition Springer-Verlag Berlin Heidelberg 1982 Math

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楼主: Bush
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Optimality in convex programming: A feasible directions approach,First-order optimality conditions for convex programming are developed using a feasible directions approach. Numerical implementations and applications are discussed. The concepts of constancy directions and minimal index set of binding constraints, central to our theory, prove useful also in studying the stability of perturbed convex programs.
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A unified theory of first and second order conditions for extremum problems in topological vector snditions of first and second order, with or without differentiability assumptions, are derived for special cases of the general problem (P). Classical results are refined and new ones are added. Second order sufficient condition, under differentiability assumptions, are derived as well.
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Characterizations of optimality without constraint qualification for the abstract convex program, a closed convex cone and . and . are topological linear spaces. We present primal and dual characterizations for (P). These characterizations are derived by reducing the problem to a standard Lagrange multiplier problem. Examples given include operator constrained problems as well as semi-infinite programming problems.
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Refinements of necessary optimality conditions in nondifferentiable programming II,ondifferentiable data. The relative generalized Jacobian matrix of a locally Lipschitz function and the normal subcone to a set defined by equalities are the principal concepts upon which our study is based.
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Mathematical Programming Studieshttp://image.papertrans.cn/o/image/703023.jpg
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