An iterative algorithm based on the piecewise linear system for solving bilateral obstacle problems

Abstract

In this paper, we derive the piecewise linear system (PLS) associated with the bilateral obstacle problem and illustrate the equivalence between the linear system and finite-dimensional complementary problem. The existence and the uniqueness of the solution to the PLS are also demonstrated. Based on the PLS, a Picard iterative algorithm is proposed. The convergence analysis is given and examples are presented to verify the effectiveness of the method.

Keywords:

• bilateral obstacle problem
• piecewise linear system
• active set strategy
• complementarity problem
• Picard-type iterative method

2000 AMS Subject Classifications::

• 65k10
• 90c33