A note on a globally convergent Newton method for solving monotone variational inequalities |
| |
| Institution: | 1. Collége Militaire Royal de Saint-Jean, Saint-Jean-sur-Richelieu, Que, Canada J1K 2R1;2. GERAD, Ecole des Hautes Etudes Commerciales, Montreal, Que., Canada H3T 1V6;1. DICATAM, Università degli Studi di Brescia, via Branze 38, 25123 Brescia, Italy;2. MOX, Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;1. ADINA R & D, Inc., 71 Elton Ave, Watertown, MA 02472, USA;2. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;1. Samsung Electronics Co., Giheung Campus, Nongseo-dong, Giheung-gu, Yongin-si, Gyeonggi-do 446-711, Republic of Korea;2. Interdisciplinary Program in Computational Science & Technology, Seoul National University, Seoul 151-747, Republic of Korea;3. Department of Mathematics and Interdisciplinary Program in Computational Science & Technology, Seoul National University, Seoul 151-747, Republic of Korea |
| |
| Abstract: | It is well-known (see Pang and Chan 8]) that Newton's method, applied to strongly monotone variational inequalities, is locally and quadratically convergent. In this paper we show that Newton's method yields a descent direction for a non-convex, non-differentiable merit function, even in the absence of strong monotonicity. This result is then used to modify Newton's method into a globally convergent algorithm by introducing a linesearch strategy. Furthermore, under strong monotonicity (i) the optimal face is attained after a finite number of iterations, (ii) the stepsize is eventually fixed to the value one, resulting in the usual Newton step. Computational results are presented. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
