Asymptotic analysis of scalarization functions and applications

Abstract

In this paper, we consider two common scalarization functions and their applications via asymptotic analysis. We mainly analyze the recession and asymptotic properties of translation invariant function and oriented distance function, and discuss their monotonicity and Lipschitz continuity in terms of recession functions. Finally, we apply these scalarization functions to the characterization of the nonemptiness and boundedness of the solution set for a general constrained nonconvex optimization problem.