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On strong KKT type sufficient optimality conditions for multiobjective semi-infinite programming problems with

Sy-Ming Guu1,2, Yadvendra Singh3, Shashi Kant Mishra3

  • 1Graduate Institute of Business and Management, College of Management, Chang Gung University, Kwei-Shan District, Taoyuan City, Taiwan, ROC.

Journal of Inequalities and Applications
|December 5, 2017
PubMed
Summary

This study introduces stationary conditions for nonsmooth multiobjective semi-infinite programming problems with vanishing constraints. It establishes strong Karush-Kuhn-Tucker type sufficient optimality conditions for these complex optimization problems.

Keywords:
generalized convexitymathematical programs with vanishing constraintsoptimality conditionssemi-infinite programming

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Area of Science:

  • Optimization Theory
  • Mathematical Programming

Background:

  • Nonsmooth multiobjective semi-infinite programming problems with vanishing constraints (MOSIPVC) present unique challenges in optimization.
  • Existing research may not fully address the complexities of optimality conditions in these specific problem types.

Purpose of the Study:

  • To introduce and define stationary conditions for MOSIPVCs.
  • To establish strong Karush-Kuhn-Tucker (KKT) type sufficient optimality conditions for MOSIPVCs.

Main Methods:

  • Development of novel theoretical frameworks for stationary conditions.
  • Application of generalized convexity concepts to derive optimality criteria.

Main Results:

  • Introduction of specific stationary conditions tailored for MOSIPVCs.
  • Establishment of strong KKT type sufficient optimality conditions under generalized convexity.

Conclusions:

  • The proposed conditions provide valuable tools for analyzing and solving MOSIPVCs.
  • The findings advance the understanding of optimality in complex mathematical programming.