Solution Existence and Compactness Analysis for Nonsmooth Optimization Problems
研究了一类非光滑非凸优化问题的最优值和全局最优解的几何性质，给出了解集非空和/或紧的条件，并利用下水平集紧性、下有界性和强制性等性质刻画了可行集无界时解集的非空性与紧性。
Abstract This paper is concerned with the analysis of geometrical properties and behaviors of the optimal value and global optimal solutions for a class of nonsmooth optimization problems. We provide conditions under which the solution set of a nonsmooth and nonconvex optimization problem is non-empty and/or compact. We also examine related properties such as the compactness of the sublevel sets, the boundedness from below and the coercivity of the objective function to characterize the non-emptiness and the compactness of the solution set of the underlying optimization problem under the unboundedness of its associated feasible set.