On constraint qualifications for multiobjective optimization problems with vanishing constraints.

*(English)*Zbl 1354.90129
Xu, Honglei (ed.) et al., Optimization methods, theory and applications. Selected papers based on the presentations at the 9th international conference on optimization: techniques and applications, ICOTA 9, Taipei, Taiwan, December 12–16, 2013. Berlin: Springer (ISBN 978-3-662-47043-5/hbk; 978-3-662-47044-2/ebook). 95-135 (2015).

Summary: 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.

For the entire collection see [Zbl 1323.90002].

For the entire collection see [Zbl 1323.90002].

##### MSC:

90C29 | Multi-objective and goal programming |

##### Keywords:

constraint qualifications; multiobjective optimization problems; vanishing constraints; efficiency; optimality conditions
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\textit{S. K. Mishra} et al., in: Optimization methods, theory and applications. Selected papers based on the presentations at the 9th international conference on optimization: techniques and applications, ICOTA 9, Taipei, Taiwan, December 12--16, 2013. Berlin: Springer. 95--135 (2015; Zbl 1354.90129)

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