caa a22 4500 475769473 CHVBK 20180406123615.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1007/PL00011388 doi (NATIONALLICENCE)springer-10.1007/PL00011388 Oustry François Inria, 655 avenue de l'Europe, 38330 Montbonnot, France.¶e-mail: Francois.Oustry@inrialpes.fr, FR aut A second-order bundle method to minimize the maximum eigenvalue function [Elektronische Daten] [François Oustry] Abstract. : In this paper we present a nonsmooth algorithm to minimize the maximum eigenvalue of matrices belonging to an affine subspace of n×n symmetric matrices. We show how a simple bundle method, the approximate eigenvalue method can be used to globalize the second-order method developed by M.L. Overton in the eighties and recently revisited in the framework of the ?-Lagrangian theory. With no additional assumption, the resulting algorithm generates a minimizing sequence. A geometrical and constructive proof is given. To prove that quadratic convergence is achieved asymptotically, some strict complementarity and non-degeneracy assumptions are needed. We also introduce new variants of bundle methods for semidefinite programming. Springer-Verlag Berlin Heidelberg, 2000 Key words: eigenvalue optimization - semidefinite programming - convex optimization - second-order bundle methods Mathematics Subject Classification (1991): 90C25, 52A41, 65K10, 15A18 nationallicence https://doi.org/10.1007/PL00011388 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00011388 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Oustry François Inria, 655 avenue de l'Europe, 38330 Montbonnot, France.¶e-mail: Francois.Oustry@inrialpes.fr, FR aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer