A class of smoothing functions for nonlinear complementarity problems and variational inequalities

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:36255

Mangasarian, O L; Chen, C

We propose a class of smooth functions that approximate the fundamental plus function, (x){sub +} =max{l_brace}0, x{r_brace}, by twice integrating a density function. This leads to classes of smooth nonlinear equation representation of nonlinear complementarily and variational inequality problems (NCPs and Vis). Existence of an arbitrarily accurate solution for the smooth nonlinear equations as well as the NCP or VI is established, for sufficiently large value of the smoothing parameter, for any solvable NCP or VI. Newton-based algorithms are proposed for the smooth problem. For strongly monotone problems, global convergence and local quadratic convergence are established. For monotone problems, each accumulation point of the proposed algorithms solves the smooth problem. Preliminary computational results will be given.

• OSTI ID: 36255
• Report Number(s): CONF-9408161--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
MATRICES
NONLINEAR PROBLEMS
NONLINEAR PROGRAMMING
NUMERICAL SOLUTION
VARIATIONAL METHODS