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ε-Mixed type duality for nonconvex multiobjective programs with an infinite number of constraints

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  • T. Son
  • D. Kim

Abstract

Using a scalarization method, approximate optimality conditions of a multiobjective nonconvex optimization problem which has an infinite number of constraints are established. Approximate duality theorems for mixed duality are given. Results on approximate duality in Wolfe type and Mond-Weir type are also derived. Approximate saddle point theorems of an approximate vector Lagrangian function are investigated. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • T. Son & D. Kim, 2013. "ε-Mixed type duality for nonconvex multiobjective programs with an infinite number of constraints," Journal of Global Optimization, Springer, vol. 57(2), pages 447-465, October.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:2:p:447-465
    DOI: 10.1007/s10898-012-9994-0
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    References listed on IDEAS

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    1. T. Son & D. Kim & N. Tam, 2012. "Weak stability and strong duality of a class of nonconvex infinite programs via augmented Lagrangian," Journal of Global Optimization, Springer, vol. 53(2), pages 165-184, June.
    2. J. Dutta, 2005. "Necessary optimality conditions and saddle points for approximate optimization in banach spaces," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 127-143, June.
    3. T. Son & N. Dinh, 2008. "Characterizations of optimal solution sets of convex infinite programs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 147-163, July.
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    Cited by:

    1. Xiangkai Sun & Kok Lay Teo & Xian-Jun Long, 2021. "Some Characterizations of Approximate Solutions for Robust Semi-infinite Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 281-310, October.
    2. Thai Doan Chuong, 2022. "Approximate solutions in nonsmooth and nonconvex cone constrained vector optimization," Annals of Operations Research, Springer, vol. 311(2), pages 997-1015, April.
    3. N. V. Tuyen & C.-F. Wen & T. Q. Son, 2022. "An approach to characterizing $$\epsilon $$ ϵ -solution sets of convex programs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 249-269, July.
    4. Zhe Hong & Kwan Deok Bae & Do Sang Kim, 2022. "Minimax programming as a tool for studying robust multi-objective optimization problems," Annals of Operations Research, Springer, vol. 319(2), pages 1589-1606, December.
    5. C. Gutiérrez & L. Huerga & V. Novo & C. Tammer, 2016. "Duality related to approximate proper solutions of vector optimization problems," Journal of Global Optimization, Springer, vol. 64(1), pages 117-139, January.
    6. Liguo Jiao & Jae Hyoung Lee, 2018. "Approximate Optimality and Approximate Duality for Quasi Approximate Solutions in Robust Convex Semidefinite Programs," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 74-93, January.

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