A Non-Interior Continuation Algorithm for the P{sub 0} or P{sub *} LCP with Strong Global and Local Convergence Properties

Journal Article · Mon Aug 15 04:00:00 EDT 2005 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-005-0827-0· OSTI ID:21067434

We propose a non-interior continuation algorithm for the solution of the linear complementarity problem (LCP) with a P{sub 0} matrix. The proposed algorithm differentiates itself from the current continuation algorithms by combining good global convergence properties with good local convergence properties under unified conditions. Specifically, it is shown that the proposed algorithm is globally convergent under an assumption which may be satisfied even if the solution set of the LCP is unbounded.Moreover, the algorithm is globally linearly and locally superlinearly convergent under a nonsingularity assumption. If the matrix in the LCP is a P{sub *} matrix, then the above results can be strengthened to include global linear and local quadratic convergence under a strict complementary condition without the nonsingularity assumption.

• OSTI ID: 21067434
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 2 Vol. 52; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
CONVERGENCE
MATHEMATICAL SOLUTIONS
MATRICES