New calculus rules of relative subdifferentials and applications to constrained optimization problems

Abstract

This paper investigates properties and calculus rules, including new calculation formulas of chain rules and maximum-pointwise rules for the relative subdifferentials of nondifferentiable functions. Based on these properties and calculation rules, we establish novel optimality conditions without normal cones for a class of optimization problems with set constraints. These results include, among other different properties, Fritz-John and Karush-Kuhn-Tucker necessary conditions for optimization problems involving equality, inequality and set constraints. We demonstrate through illustrative examples that the obtained optimality conditions are not only sharper than the existing ones even when restricted them in a finite-dimensional setting, but also applicable under weaker qualification assumptions.