Existence and Limiting Behavior of Trajectories Associatedwith P0-equations

  • Authors:

  • M. Seetharama Gowda;M. A. Tawhid

  • Affiliations:

  • Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA. gowda@math.umbc.edu;Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA. tawhid@math.umbc.edu

  • Venue:
  • Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
  • Year:
  • 1999

Quantified Score

Hi-index 0.00

Visualization

Abstract

Given a continuous P_0-function F : R^n → R^n,we describe a method of constructing trajectories associatedwith the P_0-equation F(x) = 0. Various well known equation-basedreformulations of the nonlinear complementarity problem and thebox variational inequality problem corresponding to a continuousP_0-function lead to P_0-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI,and (d) the normal map for a BVI give raise to P_0-equationswhen the underlying function is P_0. To generate thetrajectories, we perturb the given P_0-function F toa P-function F(x, ϵ); unique solutions ofF(x, ϵ) = 0 as ϵ varies over an interval in (0, ∞) thendefine the trajectory. We prove general results on theexistence and limiting behavior of such trajectories. As special cases westudy the interior point trajectory,trajectories based on the fixed point map ofa BVI, trajectories based on the normal map of a BVI, and a trajectorybased on the aggregate function of a vertical nonlinear complementarity problem.