caa a22 4500 475769554 CHVBK 20180406123616.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1007/PL00011369 doi (NATIONALLICENCE)springer-10.1007/PL00011369 A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints [Elektronische Daten] [Thomas F. Coleman, Yuying Li] Abstract. : A trust region and affine scaling interior point method (TRAM) is proposed for a general nonlinear minimization with linear inequality constraints [8]. In the proposed approach, a Newton step is derived from the complementarity conditions. Based on this Newton step, a trust region subproblem is formed, and the original objective function is monotonically decreased. Explicit sufficient decrease conditions are proposed for satisfying the first order and second order necessary conditions.¶The objective of this paper is to establish global and local convergence properties of the proposed trust region and affine scaling interior point method. It is shown that the proposed explicit decrease conditions are sufficient for satisfy complementarity, dual feasibility and second order necessary conditions respectively. It is also established that a trust region solution is asymptotically in the interior of the proposed trust region subproblem and a properly damped trust region step can achieve quadratic convergence. Springer-Verlag Berlin Heidelberg, 2000 Key words: trust region - interior point method - Dikin-affine scaling - Newton step nationallicence Coleman Thomas F. Cornell University, Comp. Sc. Dept. and Ctr. Appl. Math., 647 Rhodes Hall, Ithaca, NY 14853, USA, e-mail: coleman@tc.cornell.edu, US aut Li Yuying Computer Science Dept., Cornell University, USA, US aut https://doi.org/10.1007/PL00011369 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00011369 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Coleman Thomas F. Cornell University, Comp. Sc. Dept. and Ctr. Appl. Math., 647 Rhodes Hall, Ithaca, NY 14853, USA, e-mail: coleman@tc.cornell.edu, US aut NATIONALLICENCE 700 1- Li Yuying Computer Science Dept., Cornell University, USA, US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer