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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.
List of contents
Seeking Feasibility.- Preliminaries.- Seeking Feasibility in Linear Programs.- Seeking Feasibility in Mixed-Integer Linear Programs.- A Brief Tour of Constraint Programming.- Seeking Feasibility in Nonlinear Programs.- Analyzing Infeasibility.- Isolating Infeasibility.- Finding the Maximum Feasible Subset of Linear Constraints.- Altering Constraints to Achieve Feasibility.- Applications.- Other Model Analyses.- Data Analysis.- Miscellaneous Applications.- Epilogue.
Summary
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.
Additional text
From the reviews:
"This book is really the first monograph to summarize the growing body of research on the analysis of feasibility and infeasibility of optimization problems. With up to date coverage and very thorough bibliography, it will be of definite interest to researchers working in this area. The book may also be of interest to those readers who are more interested in modeling and applications but want to learn something about techniques for analyzing the feasibility of optimization models." (Brian Borchers, MathDL, March, 2008)
Report
From the reviews:
"This book is really the first monograph to summarize the growing body of research on the analysis of feasibility and infeasibility of optimization problems. With up to date coverage and very thorough bibliography, it will be of definite interest to researchers working in this area. The book may also be of interest to those readers who are more interested in modeling and applications but want to learn something about techniques for analyzing the feasibility of optimization models." (Brian Borchers, MathDL, March, 2008)
