Abstract
In this paper, weak sharp solutions are investigated for a variational-type inequality governed by (rho , mathbf{b}, mathbf{d})-convex path-independent curvilinear integral functional. Moreover, an equivalence between the minimum principle sufficiency property and the weak sharpness property of the solution set associated with the considered variational-type inequality is established.
Highlights
1 Introduction Based on the works of Burke and Ferris [3], Patriksson [11] and following Marcotte and Zhu [10], the concept of weak sharp solution associated with variational-type inequalities has attracted the attention of many researchers
By using gap-type functions, in accordance with Ferris and Mangasarian [5] and following Hiriart-Urruty and Lemaréchal [6], Alshahrani et al [1] studied the minimum and maximum principle sufficiency properties associated with nonsmooth variational inequalities
In this paper, motivated and inspired by the ongoing research in this field and by using some variational techniques developed in Ansari [2], Clarke [4] and Treanţă [12,13,14,15,16], we investigate a new class of variational-type inequalities governed by (ρ, b, d)-convex pathindependent curvilinear integral functionals
Summary
Based on the works of Burke and Ferris [3], Patriksson [11] and following Marcotte and Zhu [10], the concept of weak sharp solution associated with variational-type inequalities has attracted the attention of many researchers (see, for instance, Hu and Song [7], Liu and Wu [9], Zhu [17] and Jayswal and Singh [8]). Under some working assumptions and using a dual gap-type functional, the weak sharpness property of the solution set for the considered variational-type inequality is studied. In this regard, two characterization results are formulated and proved.
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