Optimality conditions in optimization problems with convex feasible set using convexificators

Alireza Kabgani, Majid Soleimani-damaneh () and Moslem Zamani
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Alireza Kabgani: University of Tehran
Majid Soleimani-damaneh: University of Tehran
Moslem Zamani: University of Tehran

Mathematical Methods of Operations Research, 2017, vol. 86, issue 1, No 4, 103-121

Abstract: Abstract In this paper, we consider a nonsmooth optimization problem with a convex feasible set described by constraint functions which are neither convex nor differentiable nor locally Lipschitz necessarily. Utilizing upper regular convexificators, we characterize the normal cone of the feasible set and derive KKT type necessary and sufficient optimality conditions. Under some assumptions, we show that the set of KKT multipliers is bounded. We also characterize the set of optimal solutions and introduce a linear approximation corresponding to the original problem which is useful in checking optimality. The obtained outcomes extend various results existing in the literature to a more general setting.

Keywords: Convex optimization; Nonsmooth optimization; Convexificator; KKT conditions; Linear approximation (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00186-017-0584-2

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