Characterization of weakly sharp solutions of a variational-type inequality with convex functional

Weak Sharp Type Solutions for Some Variational Integral Inequalities

“…Knowing the implications of variational analysis in multifarious fields, like optimization or control theory, and taking into account some techniques presented by Clarke [8], Treanţȃ [9][10][11][12][13][14][15], Jayswal and Singh [16], Kassay and Rȃdulescu [17], Mititelu and Treanţȃ [18], in this paper, we investigate weak sharp type solutions for a family of variational integral inequalities defined by a convex functional of the multiple integral type. A connection with the sufficiency property associated with the minimum principle is formulated, as well.…”

On weak sharp solutions in $(\rho , \mathbf{b}, \mathbf{d})$-variational inequalities

“…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]). Recently, 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.…”

Weak sharpness and finite convergence for mixed variational inequalities

“…Later, weak sharpness of solutions and its applications to the finite convergence property of methods for finding solutions of varitional inequalities have been investigated by many authors (see, e.g., [3,17,23,24,26,27,32,33,34] and references therein). Some authors extended and established the concept of weak sharp solutions to general variational inequalities, e.g., set-valued variational inequalities [2,31], variational-type inequalities [19], nonsmooth variational inequalities [4] and mixed variational inequalities [16].…”