FEASIBILITY AND INFEASIBILITY IN OPTIMIZATION

Feasibility and Infeasibility in Optimization is an expository book focused on practical algorithms related to feasibility and infeasibility in optimization. Part I addresses algorithms for seeking feasibility quickly, including recent algorithms for the difficult cases of nonlinear and mixed-integer programs. Part II provides algorithms for analyzing infeasibility by isolating minimal infeasible (or maximum feasible) subsets of constraints, or by finding the best repair for the infeasibility. Part III describes surprising applications in areas such as classification, computational biology, and medicine. Connections to constraint programming are shown. A main goal is to impart an understanding of the methods so that practitioners can make immediate use of existing algorithms and software, and so that researchers can extend the state of the art and find new applications. The book is of interest to researchers, students, and practitioners across the applied sciences who are working on optimization problems. TOC:Part I: Analyzing Infeasibility.- Isolating an Infeasibility.- Methods Specific to Linear Programming.- Methods Specific to Mixed Integer Programming.- Methods Specific to Nonlinear Programming.- Finding the Maximum Feasible Subset of Linear Constraints.- Finding the Best Fix for an Infeasible System.- Part II: Reaching Feasibility Quickly.- Linear Programming.- Mixed Integer Programming.- Nonlinear Programming.- Part III: Applications.- Analyzing Unboundedness in Linear Programs.- Analyzing the Viability of Network Models.- Analyzing Multiple-Objective Linear Programs.- Data Classification and Training Neural Networks.- Applications In Statistics.- Radiation Treatment Planning.- Backtracking in Constraint Programming.- Protein Folding.- Automatic Test Assembly.- General NP-Hard Problems.