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A Farkas lemma for difference sublinear systems and quasidifferentiable programming

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Abstract

A new generalized Farkas theorem of the alternative is presented for systems involving functions which can be expressed as the difference of sublinear functions. Various other forms of theorems of the alternative are also given using quasidifferential calculus. Comprehensive optimality conditions are then developed for broad classes of infinite dimensional quasidifferentiable programming problems. Applications to difference convex programming and infinitely constrained concave minimization problems are also discussed.

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Authors and Affiliations

  1. School of Mathematics, Ballarat University College, 3350, Ballarat, Vic., Australia

    B. M. Glover

  2. School of Mathematics, University of New South Wales, Kensington, NSW, Australia

    V. Jeyakumar

  3. Lehrstuhl für Mathematik VII, Universität Mannheim, Mannheim, Germany

    W. Oettli

Authors
  1. B. M. Glover
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  2. V. Jeyakumar
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  3. W. Oettli
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Glover, B.M., Jeyakumar, V. & Oettli, W. A Farkas lemma for difference sublinear systems and quasidifferentiable programming. Mathematical Programming 63, 109–125 (1994). https://doi.org/10.1007/BF01582061

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  • DOI: https://doi.org/10.1007/BF01582061

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