A continuation method for monotone variational inequality and complementary problems: With application to linear and nonlinear programming
The Variational Inequality Problem (VIP) and its special cases (complementarity problems, continuous optimization problems, nonlinear equations) are important areas of applied mathematics due to their numerical applications. This dissertation proposes a continuation method to solve monotone VIPs and analyzes various properties of the method, including the existence, uniqueness and limiting behavior of solutions. The algorithm is then specialized for continuous optimization problems (NLPs, QPs, LPs) and complementarity problems (NCPs, LCPs, mixed LCPs). This research unifies various continuation methods for VIP-related problems in the framework of the monotone VIP. In addition, in the context of complementarity problems, the continuation method is extended to solve a more general class of problems. The new method is shown to have several advantages over currently developed interior point algorithms in the case of the LCP and LP. Extensive numerical experiments are reported which support the theory developed in the dissertation and provide practical evidence for the efficiency of the new continuation algorithms.
Operations research|Management|Mathematics|Computer science
Chen, Bintong, "A continuation method for monotone variational inequality and complementary problems: With application to linear and nonlinear programming" (1990). Dissertations available from ProQuest. AAI9112546.