MERIT FUNCTION AND GLOBAL ALGORITHM FOR BOX CONSTRAINED VARIATIONAL INEQUALITIES

Abstract

Abstract:

The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original problem is reformulated as minimization with simple constraints. Then, the authors show
that any stationary point of the optimization problem is a solution of the original problem. Finally, a descent algorithm is presented for the optimization problem, and global convergence is shown.

Key words: Box constrained variational inequalities, the KKT-conditions problem,global convergence algorithm

CLC Number:

90C33

ZHANG Li-Ping, GAO Zi-You, LAI Yan-Lian. MERIT FUNCTION AND GLOBAL ALGORITHM FOR BOX CONSTRAINED VARIATIONAL INEQUALITIES[J].Acta mathematica scientia,Series B, 2002, 22(1): 63-71.

Trendmd

References

[1]Harker P T, Pang J S. Finite-dimensional variational inequality and nonlinear complementarity problems:A survey of theory, algorithm, and applications. Mathematical Programming, 1990, 48: 161-220

[2]Kanzow C, Fukushima M. Theoretical and numerical investigation of the D-gap function for box con-strained variational inequalities. Mathematical Programming, 1998, 83: 55-87

[3]Peng J M. Global method for monotone variational inequality problems with inequality constraints. Jour-nal of Optimization Theory and Application, 1997, 95: 419-430

[4]Facchini F, Kanzow C. On unconstrained and constrained stationary points of the implicit Lagrangian (To appear in JOTA)

[5]Fukushima M. Equivalent differentiable optimization problems and recent methods for asymmetric varia-tional inequlity problems. Mathematical Programming, 1992, 53: 99-110

[6]Auslender A. Optimization: M´ethods, Num´eriques. Masson, Paris, France, 1976

[7]Ferris M C, Pang J S. Engineering and economic applications of complementarity problems. Technical Report 95-07, Computer Sciences Department, University of Wisconsin (Madison, WI, May 1995)

[8]Marcotte P. A new algorithm for solving variational inequalities with application to the traffic assignment problem. Mathematical Programming, 1985, 33: 339-351

[9]Fukushima M. Merit functions for variational inequality and complementarity problems. Preprint, Grad-uate School of Information Science, Nara Institute of science and Technology, Nara, Japan, 1995

[10]Fischer A. A special Newton-type optimization method. Optimization, 1992, 24: 269-284

[11]Geiger C, Kanzow C. On the resolution of monotone complementarity problems. Computational Opti-mization and Applications, 1996, 5: 155-173

[12]Taji K, Fukushima M. A new merit function and a successive quadratic programming algorithm for vari-ational inequality problems. SIAM Journal on Optimization, 1996, (6): 704-713