Properties of the Solution Set of Absolute Value Equations and the Related Matrix Classes

The absolute value equations (AVE) problem is an algebraic of solving . So far, most the research has focused on methods for AVE, but we address itself by analyzing properties AVE and corresponding solution set. In particular, investigate topological set, such as convexity, boundedness, or connectedness, whether it consists finitely many solutions. Further, problems related to nonnegativity solutions solvability unique solvability. can be formulated means different optimization problems, in this regard are interested how with optima, Karush–Kuhn–Tucker points, feasible these problems. We characterize matrix classes associated above mentioned inspect computational complexity recognition problem; some polynomially recognizable, others proved NP-hard. For intractable cases, propose various sufficient conditions. also post new challenging that were raised during investigation problem.