On generalized convexity and duality with a square root term

Preda, Vasile

doi:10.1007/bf01416245

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“…Many authors have discussed optimality conditions and duality results for nonlinear programming problems containing the square root of a positive semidefinite quadratic function, for example those discussed by Mond [31] and Zang and Mond [38]. Mishra et al [25] proved necessary and sufficient optimality conditions for nondifferential semi-infinite programming problems involving square root of quadratic functions, see, for more details [6,32,33,35]. Furthermore, the term with the square root of a positive semidefinite quadratic function has been replaced by a more general function, namely, the support function of a compact convex set, whose the subdifferential can be simply expressed.…”

Section: Introductionmentioning

confidence: 99%

Optimality and duality for nonsmooth semi-infinite multiobjective programming with support functions

Singh

Mishra

Lai

2017

YUGOSLAV J OPERATION

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In this paper, we consider a nonsmooth semi-infinite multiobjective programming problem involving support functions. We establish sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak, strong and strict converse duality theorems under various generalized convexity assumptions. Moreover, some special cases of our problem and results are presented.

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