Optimality conditions and duality for mathematical programming with equilibrium constraints including multiple interval-valued objective functions on Hadamard manifolds

Abstract

This paper investigates mathematical programming with equilibrium constraints including multiple interval-valued objective functions on Hadamard manifolds. In the first part, both necessary and sufficient optimality conditions for some types of efficient solutions are considered. After that, the Wolfe and Mond–Weir type dual problems are formulated and the duality relations under geodesic convexity assumptions are examined. Some examples are proposed to illustrate the results.