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On Constraint Qualifications for Multiobjective Optimization Problems with Vanishing Constraints

In: Optimization Methods, Theory and Applications

Author

Listed:
  • S. K. Mishra

    (Banaras Hindu University, Department of Mathematics)

  • Vinay Singh

    (National Institute of Technology, Department of Mathematics)

  • Vivek Laha

    (Banaras Hindu University, Department of Mathematics, Faculty of Science)

  • R. N. Mohapatra

    (University of Central Florida, Department of Mathematics)

Abstract

In this chapter, we consider a class of multiobjective optimization problems with inequality, equality and vanishing constraints. For the scalar case, this class of problems reduces to the class of mathematical programs with vanishing constraints recently appeared in literature. We show that under fairly mild assumptions some constraint qualifications like Cottle constraint qualification, Slater constraint qualification, Mangasarian-Fromovitz constraint qualification, linear independence constraint qualification, linear objective constraint qualification and linear constraint qualification do not hold at an efficient solution, whereas the standard generalized Guignard constraint qualification is sometimes satisfied. We introduce suitable modifications of above mentioned constraint qualifications, establish relationships among them and derive the Karush-Kuhn-Tucker type necessary optimality conditions for efficiency.

Suggested Citation

  • S. K. Mishra & Vinay Singh & Vivek Laha & R. N. Mohapatra, 2015. "On Constraint Qualifications for Multiobjective Optimization Problems with Vanishing Constraints," Springer Books, in: Honglei Xu & Song Wang & Soon-Yi Wu (ed.), Optimization Methods, Theory and Applications, edition 127, chapter 0, pages 95-135, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-47044-2_6
    DOI: 10.1007/978-3-662-47044-2_6
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