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1995-1996 | 117 | 2 | 123-136
Tytuł artykułu

Open mapping theorem and inversion theorem for γ-paraconvex multivalued mappings and applications

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EN
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EN
We extend the open mapping theorem and inversion theorem of Robinson for convex multivalued mappings to γ-paraconvex multivalued mappings. Some questions posed by Rolewicz are also investigated. Our results are applied to obtain a generalization of the Farkas lemma for γ-paraconvex multivalued mappings.
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Twórcy
  • Université de Bourgogne, Laboratoire "Analyse Appliquée et Optimisation", B.P. 138, 21004 Dijon Cedex, France, jourani@satie.u-bourgogne.fr
Bibliografia
  • [1] J. M. Borwein and D. M. Zhuang, Verifiable necessary and sufficient conditions for regularity of set-valued and single-valued maps, J. Math. Anal. Appl. 134 (1988), 441-459.
  • [2] F. H. Clarke, A new approach to Lagrange multipliers, Math. Oper. Res. 1 (1976), 165-174.
  • [3] R. Cominetti, Metric regularity, tangent sets and second-order optimality conditions, Appl. Math. Optim. 21 (1990), 265-288.
  • [4] S. Dolecki, Open relation theorem without closedness assumption, Proc. Amer. Math. Soc. 109 (1990), 1019-1024.
  • [5] B. M. Glover, V. Jeyakumar and W. Oettli, A Farkas lamma for difference sublinear systems and quasi-differentiable programming, Math. Programming 63 (1994), 109-125.
  • [6] J. Gwinner, Results of Farkas type, Numer. Funct. Anal. Optim. 9 (1987), 471-520.
  • [7] V. Jeyakumar, A general Farkas lemma and characterization of optimality for a nonsmooth program involving convex processes, J. Optim. Theory Appl. 55 (1987), 449-461.
  • [8] A. Jourani, Intersection formulae and the marginal function in Banach spaces, J. Math. Anal. Appl. 192 (1995), 867-891.
  • [9] A. Jourani, Subdifferentiability and subdifferential monotonicity of γ-paraconvex functions, 1995, submitted.
  • [10] A. Jourani and L. Thibault, The use of metric graphical regularity in approximate subdifferential calculus rule in finite dimensions, Optimization 21 (1990), 509-519.
  • [11] J.-P. Penot, Metric regularity, openness and Lipschitzian behavior of multifunctions, Nonlinear Anal. 13 (1989), 629-643.
  • [12] S. M. Robinson, Regularity and stability for convex multivalued functions, Math. Oper. Res. 1 (1976), 130-143.
  • [13] R. T. Rockafellar, Extensions of subgradient calculus with applications to optimization, Nonlinear Anal. 9 (1985), 665-698.
  • [14] S. Rolewicz, On paraconvex multifunctions, Oper. Res. Verfahren 31 (1979), 539-546.
  • [15] S. Rolewicz, On γ-paraconvex multifunctions, Math. Japon. 24 (1979), 293-300.
  • [16] S. Rolewicz, On conditions warranting $Φ_2$-subdifferentiability, Math. Programming Study 14 (1981), 215-224.
  • [17] K. Shimizu, E. Aiyoshi and R. Katayama, Generalized Farkas's theorem and optimization of infinitely constrained problems, J. Optim. Theory Appl. 40 (1983), 451-462.
  • [18] C. Swartz, A general Farkas lemma, ibid. 46 (1985), 237-244.
  • [19] C. Ursescu, Multifunctions with convex closed graph, Czechoslovak Math. J. 7 (1975), 438-441.
  • [20] D. E. Ward and J. M. Borwein, Nonsmooth calculus in finite dimensions, SIAM J. Control Optim. 25 (1987), 1312-1340.
  • [21] C. Zalinescu, On Gwinner's paper "Results of Farkas type", Numer. Funct. Anal. Optim. 10 (1989), 401-414.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv117i2p123bwm
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