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Characterizations and applications of generalized invexity and monotonicity in Asplund spaces

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  • M. Soleimani-damaneh

Abstract

In this paper, the concepts of invexity, monotonicity, and their generalizations in Asplund spaces are studied. Some characterizations for several kinds of generalized invexity and monotonicity concepts are given, using the properties of Mordukhovich limiting subdifferentials in Asplund spaces; and some applications in mathematical programming are provided. Also, some necessary and sufficient weak Pareto-optimality conditions for a multiple-objective optimization problem are proved. Copyright Sociedad de Estadística e Investigación Operativa 2012

Suggested Citation

  • M. Soleimani-damaneh, 2012. "Characterizations and applications of generalized invexity and monotonicity in Asplund spaces," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 592-613, October.
    • Handle: RePEc:spr:topjnl:v:20:y:2012:i:3:p:592-613
    DOI: 10.1007/s11750-010-0150-z
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    References listed on IDEAS

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    1. Soleimani-damaneh, M., 2008. "Infinite (semi-infinite) problems to characterize the optimality of nonlinear optimization problems," European Journal of Operational Research, Elsevier, vol. 188(1), pages 49-56, July.
    2. Peng, Jian-Wen, 2006. "Criteria for generalized invex monotonicities without Condition C," European Journal of Operational Research, Elsevier, vol. 170(2), pages 667-671, April.
    3. Yang, X. M. & Yang, X. Q. & Teo, K. L., 2005. "Criteria for generalized invex monotonicities," European Journal of Operational Research, Elsevier, vol. 164(1), pages 115-119, July.
    4. X.M. Yang & X.Q. Yang & K.L. Teo, 2003. "Generalized Invexity and Generalized Invariant Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 607-625, June.
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    Cited by:

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