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Characterizations of optimality without constraint qualification for the abstract convex program

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Optimality and Stability in Mathematical Programming

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 19))

Abstract

We consider the general abstract convex program (P) minimize f(x), subject to g(x)∈−S, where f is an extended convex functional on X, g: X→Y is S-convex, S is a closed convex cone and X and Y 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.

Research partially supported by NRC A4493. Presently at the Department of Mathematics, Carnegie-Mellon University, Pittsburgh, PA, U.S.A.

Research partially supported by NSERC A 3388. Presently at the Department of Mathematics, The University of Alberta, Edmonton, Alta., Canada.

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Authors and Affiliations

  1. Department of Mathematics, Dalhousie University, B3H 4H8, Halifax, N.S., Canada

    J. M. Borwein & H. Wolkowicz

Authors
  1. J. M. Borwein
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  2. H. Wolkowicz
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Monique Guignard

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© 1982 The Mathematical Programming Society, Inc.

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Borwein, J.M., Wolkowicz, H. (1982). Characterizations of optimality without constraint qualification for the abstract convex program. In: Guignard, M. (eds) Optimality and Stability in Mathematical Programming. Mathematical Programming Studies, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120983

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  • DOI: https://doi.org/10.1007/BFb0120983

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00849-8

  • Online ISBN: 978-3-642-00850-4

  • eBook Packages: Springer Book Archive

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