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Necessary conditions for nonsmooth multiobjective semi-infinite problems using Michel–Penot subdifferential

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Abstract

In this paper, for a nonsmooth multiobjective semi-infinite optimization problem, where the objective and constraint functions are locally Lipschitz, some constraint qualifications are given, and Kuhn–Tucker-type necessary optimality conditions are derived. All results are expressed in terms of Michel–Penot subdifferential.

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References

  • Borwein, J.M., Lewis, A.S.: Convex Analysis and Nonlinear Optimization: Theory and Examples. Springer, New York (2000)

    Book  Google Scholar 

  • Caristi, G., Ferrara, M., Stefanescu, A.: Semi-infinite multiobjective programming with generalized Invexity. Math. Rep. 12, 217–233 (2010)

    Google Scholar 

  • Chuong, T.D., Huy, N.Q.: Sufficient conditions for Pseudo-Lipschitz property in convex semi-infinite vector optimization problems. Nonlinear Anal. TMA 71, 6312–6322 (2009)

    Article  Google Scholar 

  • Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, Interscience (1983)

    Google Scholar 

  • Fan, X., Cheng, C., Wang, H.: Density of stable convex semi-infinite vector optimization problems. Oper. Res. Lett. 40, 140–153 (2012)

    Article  Google Scholar 

  • Giorgi, G., Guerraggio, A., Thierselder, J.: Mathematics of Optimization. Elsevier, Smooth and Nonsmooth cases (2004)

    Google Scholar 

  • Glover, B.M., Jeyakumar, V., Rubinov, A.M.: Dual conditions characterizing optimality for convex multi-objective problems. Math. Program. 84, 201–217 (1999)

    Article  Google Scholar 

  • Goberna, M.A., López, M.A.: Linear Semi-Infinite Optimization. Wiley, Chichester (1998)

    Google Scholar 

  • Hettich, R., Kortanek, O.: Semi-infinite programming: theory, methods, and applications. Siam Rev. 35, 380–429 (1993)

    Article  Google Scholar 

  • Hiriart-Urruty, J.B., Lemarechal, C.: Convex Analysis and Minimization Algorithms, I & II. Springer, Berlin (1991)

    Google Scholar 

  • Jeyakumar, V., Luc, T.D.: Nonsmooth Vector Functions and Continuous Optimization, Springer, Optimization and Its Applications, vol. 10. Springer, New York (2008)

    Google Scholar 

  • Kanzi, N.: Constraint qualifications in semi-infinite systems and their applications in nonsmooth semi-infinite problems with mixed constraints. SIAM J. Optim. 24, 559–572 (2014)

    Article  Google Scholar 

  • Kanzi, N., Nobakhtian, S.: Optimality conditions for nonsmooth semi-infinite multiobjective programming. Optim. Lett. 8, 1517–1528 (2014)

    Article  Google Scholar 

  • Kanzi, N.: Necessary optimality conditions for nonsmooth semi-infinite programming problems. J. Glob. Optim. 49, 713–725 (2011)

    Article  Google Scholar 

  • López, M.A., Still, G.: Semi-infinite programming. Eur. J. Op. Res. 180, 491–518 (2007)

    Article  Google Scholar 

  • López, M.A., Vercher, E.: Optimality conditions for nondifferentiable convex semi-infinite programming. Math. Program. 27, 307–319 (1983)

    Article  Google Scholar 

  • Maeda, T.: Constraint qualifications in multiobjective optimization problems: differentiable case. J. Optim. Theory Appl. 80, 483–500 (1994)

    Article  Google Scholar 

  • Michel, P., Penot, J.P.: Calcul sous-differentiel pour des fonctions lipschitziennes et non lipschitziennes. C.R. Acad. Sci. Paris sér. I Math. 12, 269–272 (1984)

    Google Scholar 

  • Michel, P., Penot, J.P.: A Generalized derivative for calm and stable functions. Diff. Integral Equ. 5, 433–454 (1992)

    Google Scholar 

  • Reemtsen, R., Rückmann, J.J. (eds.): Semi-infinite programming. Nonconvex optimization and its applications. 15, Kluwer Academic Publishers, Boston (1998)

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Caristi, G., Ferrara, M. Necessary conditions for nonsmooth multiobjective semi-infinite problems using Michel–Penot subdifferential. Decisions Econ Finan 40, 103–113 (2017). https://doi.org/10.1007/s10203-017-0186-8

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  • DOI: https://doi.org/10.1007/s10203-017-0186-8

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