On minty variational principle for quasidifferentiable vector optimization problems

On quasidifferentiable mathematical programs with equilibrium constraints

“…The notion of generalized convexity introduced by Singh and Laha [41] which unifies the functions introduced by Antczak [2] and by Nobakhtian [38] has been used to explore the criteria under which a 𝑊−stationary point becomes a global (or a local) minimizer of the QMPEC. Further, some other constraint qualifications and stationary conditions [16,18,22,36,44] under different generalized convexity assumptions [26,34,35,42] can be investigated for the QMPEC. Moreover, quasidifferentiable analaysis can be used to solve mathematical programs with vanishing constraints [29,30,33,37] involving quasidifferentiable functions.…”

“…Baier et al [4] looked at directed and Rubinov subdifferentials of quasidifferentiable functions. Some recent interesting results in the field of quasidifferentiable programming is due to Antczak [2,3], Abbasov [1], Dolgopolik [12,13], Lin et al [27], Singh and Laha [41,42] which have induced further scope of study.…”

On Approximate Variational Inequalities and Bilevel Programming Problems

“…Variational inequalities have several applications in the fields of economics, game theory, and traffic analysis (see [38,39] and the references cited therein). Variational inequality problems have been studied by several scholars as tools for solving optimization problems, for more exposition (see, [40][41][42][43][44][45][46][47][48][49][50][51][52] in the Euclidean space setting and [53][54][55] on Hadamard manifolds). Komlósi [56] derived the equivalence among the solutions of Minty and Stampacchia variational inequality and the optimal solution of the minimization problem.…”