SOLVING A MINIMIZATION PROBLEM FOR A CLASS OF CONSTRAINED MAXIMUM EIGENVALUE FUNCTION

Abstract

Nonsmooth convex optimization problem is a class of important problems in operational research. Bundle methods are considered as one of the most efficient methods for solving nonsmooth optimization problems. The methods have already been applied to many practical problems. In this paper, using bundle method, the optimization problem that the sum of maximum eigenvalue function and general non-smooth convex function can be solved. Through approximation to the objective function, the proximal bundle method based on approximate model is given. We prove that the sequences generated by the algorithm converge to the optimal solution of the original problem. Finally, the algorithm is used to solve a class of constrained maximum eigenvalue function.