A VU-DECOMPOSITION TECHNIQUE FOR A CLASS OF EIGENVALUE OPTIMIZATIONS

摘要

The past decade has seen the tremendous development of a number of classes of nonsmooth functions, especially those possess smooth substructure, such as max-type functions and maximum eigenvalue functions. In this paper, we mainly consider a special class of eigenvalue optimization problems: the arbitrary eigenvalue functions. For this class of functions, we can extract this property of smooth part similarly. We give second-order expansions for this class of nonsmooth functions from the VU-space decomposition point of view. A new U-Lagrangian function is proposed, and expressions for the associated second-order objects are given in terms of U-subspace Hessians. Moreover, we explore an algorithmic framework with superlinear convergence.