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Necessary optimality conditions for robust nonsmooth multiobjective optimization problems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper deals with a robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions. Under an appropriate constraint qualification, we establish necessary optimality conditions for weakly robust efficient solutions of the considered problem. These optimality conditions are presented in terms of Karush-Kuhn-Tucker multipliers and convexificators of the related functions. Examples illustrating our findings are also given.
Rocznik
Strony
289--302
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
  • LAMA, FSDM, Sidi Mohamed Ben Abdellah University, Fes, Morocco
autor
  • LAMA, FSDM, Sidi Mohamed Ben Abdellah University, Fes, Morocco
Bibliografia
  • Apostol, T.M. (2004) Mathematical Analysis, Second Edition. Pearson Education Asia Limited and China Machine.
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  • Bokrantz, R. and Fredriksson, A. (2017) Necessary and sufficient conditions for Pareto efficiency in robust multiobjective optimization. European Journal of Operational Research 262, 682–692.
  • Chen, J., Köbis, E. and Yao, J.C. (2019) Optimality conditions and duality for robust nonsmooth multiobjective optimization problems with constraints. Journal of Optimization Theory and Applications 181, 411–436.
  • Chuong, T.D. (2016) Optimality and duality for robust multiobjective optimization problems. Nonlinear Analysis 134, 127–143.
  • Clarke, F.C. (1983) Optimization and Nonsmooth Analysis. New York, Wiley-Interscience.
  • Craven, B.D. and Islam, S.M. (2012) Linear programming with uncertain data: Some extensions to robust optimization. Journal of Optimization Theory and Applications 155, 673–679.
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  • Dutta, J. and Chandra, S. (2002) Convexifactors, generalized convexity, and optimality conditions. Journal of Optimization Theory and Applications 113, 41–64.
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  • Ewing, G.M. (1977) Sufficient conditions for global minima of suitably convex functionals from variational and control theory. SIAM Review 19, 202–220.
  • Gadhi, N.A. (2021) Comments on “A Note on the Paper “Optimality Conditions for Optimistic Bilevel Programming Problem Using Convexifac tors””. Accepted for publication in Journal of Optimization Theory and Applications.
  • Gadhi, N. A. and Ichatouhane, A. (2021) A note on the paper “Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming”. RAIRO-Oper. Res. 55, 13–22.
  • Hiriart-Urruty, J.B. and Lemarechal, C. (2001) Fundamentals of Convex Analysis. Springer-Verlag, Berlin Heidelberg.
  • Jeyakumar, V. and Luc, D.T. (1999) Nonsmooth calculus, minimality, and monotonicity of convexificators. Journal of Optimization Theory and Applications 101, 599–621.
  • Jeyakumar, V., Li, G. and Lee, G. M. (2012) Robust duality for generalized convex programming problems under data uncertainty. Nonlinear Analysis 75, 1362–1373.
  • Kabgani, A. and Soleimani-damaneh, M. (2017) Characterization of (weakly/properly/robust) efficient solutions in nonsmooth semiinfinite multiobjective optimization using convexificators. Optimization 67, 217–235.
  • Kabgani, A. and Soleimani-damaneh, M. (2019) Constraint qualifications and optimality conditions in nonsmooth locally star-shaped optimization using convexificators. Pacific Journal of Optimization 15, 399–413.
  • Kanzi N. (2011) Necessary optimality conditions for nonsmooth semi-infinite programming problems. Journal of Global Optimization 49, 713–725.
  • Kaur S. (1983) Theoretical studies in mathematical programming. PhD thesis. University of Delhi.
  • Kuroiwa, D. and Lee, G. M. (2012) On robust multiobjective optimization. Vietnam Journal of Mathematics 40, 305–317.
  • Lee, G. M. and Son, P.T. (2014) On nonsmooth optimality theorems for robust optimization problems. Bulletin of the Korean Mathematical Society 51, 287–301.
  • Li, X. F. and Zhang, J. Z. (2006) Necessary optimality conditions in terms of convexificators in Lipschitz optimization. Journal of Optimization Theory and Applications 131, 429–452.
  • Li, C., Ng, K.F. and Pong T.K. (2008) Constraint qualifications for convex inequality systems with applications in constrained optimization. SIAM Journal on Optimization 19, 163–187.
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  • Saadati, M. and Oveisiha, M. (2021) Optimality conditions for robust nonsmooth multiobjective optimization problems in Asplund spaces. arXiv preprint arXiv:2105.14366.
  • Tung, L.T. (2020) Karush-Kuhn-Tucker optimality conditions and duality for convex semi-infinite programming with multiple interval-valued objective functions. Journal of Applied Mathematics and Computing 62, 67–91.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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