Optimality and duality in vector optimization involving generalized type I functions over cones

Abstract

Vector optimization, Cones, Invexity, Type-I functions, Optimality, Duality,

Robust duality for generalized convex nonsmooth vector programs with uncertain data in constraints

“…Quasi-convex functions have several applications in signal processing and machine learning. Motivated by the definitions of generalized convexity introduced in [4,11,18], we introduce the following class of functions. Definition 1.3.…”

“…However, for data uncertain problems over cones, Chen et al [4] defined type-I generalized convex functions to study optimality conditions and duality results. Suneja et al [18] have introduced various classes of nonsmooth generalized convex functions to study mathematical programs where data uncertainty is not incorporated. In this article, we introduce generalized pseudo-quasi type-I-convex functions and illustrate with non-trivial numerical examples.…”

Optimality Conditions and Dualities for Robust Efficient Solutions of Uncertain Set-Valued Optimization with Set-Order Relations

“…Recently, the dual theorem in the face of data uncertainty has received a great deal of attention due to the reality of uncertainty in many real-world optimization problems. Suneja et al [28] constructed strong/weak duality results between the primary problem and its Mond-Weir type dual problem using Clarke's generalized gradients and sufficient optimality criteria for the vector optimization problems. Chuong and Kim [29] established sufficient conditions for (weakly) efficient solutions of a nonsmooth semi-infinite multiobjective optimization problem and proposed types of Wolfe and Mond-Weir dual problems via the limiting subdifferential of locally Lipschitz functions.…”

On a Nondifferentiable Vector Optimization Involving Semi $E$-Type-I Maps in Banach Spaces

“…See, e.g., [1,2]. Many attempts have been made during the past several decades to weaken convexity hypothesis [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. In this endeavor, Hanson and Mond [6] introduced a new class of functions called type-I function for a scalar optimization problem, which was further generalized to pseudotype-I and quasi-type-I by Rueda and Hanson [7].…”

“…Recently, Anurag Jayswal [16] introduced new classes of generalized α-univex type-I vector-valued functions and obtained several K-T type sufficient optimality conditions and Mond-Weir type duality results for a multiobjective programming problem with inequality constraints. More recently, Suneja et al [17] defined generalized type-I functions over cones and established sufficient optimality conditions and duality results for a vector minimization problem using Clarkes generalized gradients. Especially, Yu and Liu [18] obtained some sufficient optimality conditions and duality results for a differentiable vector problem with inequality constraint involving the generalized type-I maps in Banach spaces.…”