Optimality Conditions and Lagrange Dualities for Optimization Problems Involving Φc-convex Functions - Hu, Ling-Li; Fang, Dong-Hui (Journal of optimization theory and applications, 2025)
In this paper, we consider an optimization problem in which the objective is the difference of two Φc-convex functions and the constraints include a set constraint and a cone constraint. We first introduce three new constraint qualifications regarding the c-subdifferential and the epigraph properties of the involved functions. Under the new constraint qualifications, we provide some sufficient conditions for optimality conditions to hold. Similarly, strong and total Lagrange dualities for the optimization problem involving the difference of two Φc-convex functions are also given.