Complementarity: Applications, Algorithms and Extensions: (50 Applied Optimization)

This volume contains a collection of papers from experts in the field of complementarity on state-of-the-art applications, algorithms, extensions and theory, resulting in a contemporary view of the complete field of complementarity. The impact of complementarity in such diverse fields as deregulation of electricity markets, engineering mechanics, optimal control and asset pricing is described using both survey and current research articles. The papers outline problem classes where complementarity can be used to model both physical and structural phenomena in ways that lead to new solution approaches. The novel application of complementarity and optimization ideas to problems in the burgeoning fields of machine learning and data mining is covered. New algorithmic advances including preprocessing and nonmonotone searches, extensions of computational methods using tools from nonsmooth analysis, and related theory for mathematical programs with equilibrium constraints is also detailed.

Table of Contents:
Approximating Maximum Stable Set and Minimum Graph Coloring Problems with the Positive Semidefinite Relaxation.- Nonmonotone Path Following Methods for Nonsmooth Equations and Complementarity Problems.- Scalable Probabilistic Clustering.- A complementarity eigenproblem in the stability analysis of finite dimensional elastic systems with frictional contact.- Variational Inequality Models of Restructured Electricity Systems.- Optimization Approaches to Semi-Supervised Learning.- Preprocessing Complementarity Problems.- On the Connectedness of Solution Sets of Parametrized Equations and of Solution Sets in Linear Complementarity Problems.- An Active Set-type Newton Method for Constrained Nonlinear Systems.- Mathematical Programming in Engineering Mechanics: Some Current Problems.- Data Discrimination via Nonlinear Generalized Support Vector Machines.- On Constraint Qualifications for Mathematical Programs with Mixed Complementarity Constraints.- A Generation Operation Planning Model in Deregulated Electricity Markets based on the Complementarity Problem.- A Class of Globally Convergent Algorithms for Pseudomonotone Variational Inequalities.- Successive Convex Relaxation Approach to Bilevel Quadratic Optimization Problems.- On a Nonsmooth Newton Method for Nonlinear Complementarity Problems in Function Space with Applications to Optimal Control.- The Proximal Point Algorithm for the P0 Complementarity Problem.- Free Boundary Problems in Asset Pricing with Transaction Costs.