Recession function and its applications in optimization. (2nd December 2021) - Li, Genghua; Li, Shengjie; You, Manxue
ABSTRACT: In this paper, we focus on the recession cone and recession function in the nonconvex case. By virtue of the recession function, we investigate the monotonicity of a function. Then, we obtain a characterization of the Lipschitz continuity for a function by using the recession function. As applications, we study the monotonicity and Lipschitz continuity properties of the optimal value function for a parametric constrained optimization problem. Moreover, we present a characterization of the nonemptiness and boundedness of the solution set for a constrained optimization problem without convexity assumption.