Sufficient conditions of optimality for multiobjective optimization problems with γ-paraconvex data

T. Amahroq; A. Taa

Studia Mathematica (1997)

  • Volume: 124, Issue: 3, page 239-247
  • ISSN: 0039-3223

Abstract

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We study multiobjective optimization problems with γ-paraconvex multifunction data. Sufficient optimality conditions for unconstrained and constrained problems are given in terms of contingent derivatives.

How to cite

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Amahroq, T., and Taa, A.. "Sufficient conditions of optimality for multiobjective optimization problems with γ-paraconvex data." Studia Mathematica 124.3 (1997): 239-247. <http://eudml.org/doc/216411>.

@article{Amahroq1997,
abstract = {We study multiobjective optimization problems with γ-paraconvex multifunction data. Sufficient optimality conditions for unconstrained and constrained problems are given in terms of contingent derivatives.},
author = {Amahroq, T., Taa, A.},
journal = {Studia Mathematica},
keywords = {contingent derivative; γ-paraconvex multifunction; optimality conditions; B-tangentially compact; compactly γ-paraconvex multifunction; Pareto minimal point; sufficient optimality conditions; multiobjective optimization; -paraconvex multifunction data; contingent derivatives},
language = {eng},
number = {3},
pages = {239-247},
title = {Sufficient conditions of optimality for multiobjective optimization problems with γ-paraconvex data},
url = {http://eudml.org/doc/216411},
volume = {124},
year = {1997},
}

TY - JOUR
AU - Amahroq, T.
AU - Taa, A.
TI - Sufficient conditions of optimality for multiobjective optimization problems with γ-paraconvex data
JO - Studia Mathematica
PY - 1997
VL - 124
IS - 3
SP - 239
EP - 247
AB - We study multiobjective optimization problems with γ-paraconvex multifunction data. Sufficient optimality conditions for unconstrained and constrained problems are given in terms of contingent derivatives.
LA - eng
KW - contingent derivative; γ-paraconvex multifunction; optimality conditions; B-tangentially compact; compactly γ-paraconvex multifunction; Pareto minimal point; sufficient optimality conditions; multiobjective optimization; -paraconvex multifunction data; contingent derivatives
UR - http://eudml.org/doc/216411
ER -

References

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  1. [1] K. Allali and T. Amahroq, On openness and regularity of γ-paraconvex multifunctions, Control Cybernet., to appear. Zbl0891.49008
  2. [2] T. Amahroq and L. Thibault, On proto-differentiability and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems, Numer. Funct. Anal. Optim. 16 (1995), 1293-1307. Zbl0857.49011
  3. [3] J. P. Aubin, Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions, Adv. in Math. Suppl. Stud. 7a, L. Nachbin (ed.), Academic Press, New York, 1981, 159-229. 
  4. [4] H. W. Corley, Optimality conditions for maximizations of set valued-functions, J. Optim. Theory Appl. 58 (1988), 1-10. Zbl0956.90509
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  6. [6] D. T. Luc, Contingent derivatives of set-valued maps and applications to vector optimization, Math. Programming 50 (1991), 99-111. Zbl0718.90080
  7. [7] D. T. Luc and C. Malivert, Invex optimisation problems, Bull. Austral. Math. Soc. 46 (1992), 47-66. Zbl0755.90072
  8. [8] J. P. Penot, Differentiability of relations and differential stability of perturbed optimization problems, SIAM J. Control Optim. 22 (1984), 529-551. Zbl0552.58006
  9. [9] S. Rolewicz, On paraconvex multifunctions, Oper. Res. Verfahren 31 (1979), 539-546. Zbl0403.49021
  10. [10] S. Rolewicz, On γ-paraconvex multifunctions, Math. Japon. 24 (1979), 293-300. Zbl0434.54009
  11. [11] D. S. Shi, Contingent derivative of the perturbation map in multiobjective optimization, J. Optim. Theory Appl. 70 (1991), 385-396. Zbl0743.90092
  12. [12] A. Taa, Necessary and sufficient conditions for multiobjective optimization problems, Optimization 36 (1996), 97-104. Zbl0858.90112
  13. [13] T. Tanino, Sensitivity analysis in multiobjective optimization, J. Optim. Theory Appl. 56 (1988), 479-499. Zbl0619.90073

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