Generalized (p, r)-Invexity in Mathematical Programming

On G-invexity-type nonlinear programming problems

“…The term invex (which means invariant convex) was suggested later by Craven [10]. Over the years, many generalizations of this concept have been given in the literature (see, for instance, [1], [2], [3], [5], [6], [7], [8], [9], [12], [13], [14], [15], [16], and others).…”

The Notion of V-r-Invexity in Differentiable Multiobjective Programming

“…To relax convexity assumptions imposed in theorems on sufficient optimality conditions and duality, various generalized convexity notions have been proposed (see, for example, [2], [3], [4], [12], [15], [17], [21], [23]). …”

“…After the works of Hanson and Craven, other types of differentiable functions have appeared with the intent of generalizing invex functions from different points of view. One of such generalizations is r-invexity which was introduced by Antczak [4]. Many authors have studied some properties and further generalizations of scalar Hanson's functions to vector-valued functions, in view of applications to multiobjective optimization problems.…”

“…Basing on the definition of V -invex vector-valued functions and the definition of scalar r-invex functions [4], we introduce a new class of differentiable nonconvex vector valued functions, namely V -r-invex functions with respect to η.…”

Exponential type vector variational-like inequalities and nonsmooth vector optimization problems

“…Thereafter, Reiland [16] defined invexity for Lipschitz real-valued functions in terms of Clarke's generalized gradient. Antczak [4] broadened the concept of Lipschitz functions to a new class of (Lipschitz) r -invex functions, which subsumes the class of Lipschitz invex functions defined by Reiland [16] and generalizes the definition of differentiable r -invex functions to the case of (nondifferentiable) Lipschitz functions.…”