A Fast Space-decomposition Scheme for Nonconvex Eigenvalue Optimization |
| |
Authors: | Ming Huang Li-Ping Pang Yuan Lu Zun-Quan Xia |
| |
Institution: | 1.Department of Mathematics,Dalian Maritime University,Dalian,China;2.School of Control Science and Engineering,Dalian University of Technology,Dalian,China;3.CORA, School of Mathematical Sciences,Dalian University of Technology,Dalian,China;4.College of Science,Shenyang University,Shenyang,China |
| |
Abstract: | In this paper, a nonsmooth bundle algorithm to minimize the maximum eigenvalue function of a nonconvex smooth function is presented. The bundle method uses an oracle to compute separately the function and subgradient information for a convex function, and the function and derivative values for the smooth mapping. Using this information, in each iteration, we replace the smooth inner mapping by its Taylor-series linearization around the current serious step. To solve the convex approximate eigenvalue problem with affine mapping faster, we adopt the second-order bundle method based on ????-decomposition theory. Through the backtracking test, we can make a better approximation for the objective function. Quadratic convergence of our special bundle method is given, under some additional assumptions. Then we apply our method to some particular instance of nonconvex eigenvalue optimization, specifically: bilinear matrix inequality problems. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|