Probability-One Homotopy Maps for Mixed Complementarity Problems

Files
TR Number
Date
2007-03-19
Journal Title
Journal ISSN
Volume Title
Publisher
Virginia Tech
Abstract

Probability-one homotopy algorithms have strong convergence characteristics under mild assumptions. Such algorithms for mixed complementarity problems (MCPs) have potentially wide impact because MCPs are pervasive in science and engineering. A probability-one homotopy algorithm for MCPs was developed earlier by Billups and Watson based on the default homotopy mapping. This algorithm had guaranteed global convergence under some mild conditions, and was able to solve most of the MCPs from the MCPLIB test library. This thesis extends that work by presenting some other homotopy mappings, enabling the solution of all the remaining problems from MCPLIB. The homotopy maps employed are the Newton homotopy and homotopy parameter embeddings.

Description
Keywords
optimization, complementarity, nonlinear embedding, Newton homotopy, globally convergent
Citation
Collections