Post-Optimal Analysis in Linear Semi-Infinite Optimization examines the following topics in regards to linear semi-infinite optimization: modeling uncertainty, qualitative stability analysis, quantitative stability analysis and sensitivity analysis. Linear semi-infinite optimization (LSIO) deals with linear optimization problems where the dimension of the decision space or the number of constraints is infinite. The authors compare the post-optimal analysis with alternative approaches to uncertain LSIO problems and provide readers with criteria to choose the best way to model a given uncertain LSIO problem depending on the nature and quality of the data along with the available software. This work also contains open problems which readers will find intriguing a challenging. Post-Optimal Analysis in Linear Semi-Infinite Optimization is aimed toward researchers, graduate and post-graduate students of mathematics interested in optimization, parametric optimization and related topics.

Depicts modeling uncertainty, qualitative stability analysis, quantitative stability analysis and sensitivity analysis in relation to linear semi-infinite optimization Emphasizes main concepts, results and technical aspects of linear semi-infinite optimization to readers in various fields Contains recent results on the emerging quantitative stability and sensitivity theories

Autorentext

Francisco J. Aragón-Artacho is an associate professor of statistics and operations research at the University of Alicante, Spain. After obtaining a PhD in Mathematics at the University of Murcia in 2007, he worked as an analyst for a private business company in Madrid for nearly a year. Subsequently, he held several postdoctoral positions at the University of Alicante, University of Newcastle (Australia) and the Luxembourg Centre for Systems Biomedicine. His main research topics are in the area of convex and set-valued analysis, with special emphasis in the development of optimization and feasibility algorithms. He has published 39 research papers and the textbook Nonlinear Optimization (Springer, 2019), coauthored by M.A Goberna, M.A. López, and M.M.L. Rodríguez. Possibly his best-known work is Walking on real numbers (Math. Intelligencer 35, 2013), coauthored with D.H. Bailey, J.M Borwein and P.B. Borwein, which features a massive image generated on the first100 billion base-4 digits of . He has served as Associate Editor for the journals Optimization Letters (since 2022) and Fixed Point Theory (since 2021). Miguel A. Goberna is an emeritus professor of statistics and operations research at the University of Alicante, Spain. He received a PhD in Mathematics in 1979 from the University of Valencia. His main research areas appear in the title, Geometry, Optimization, and Convex Analysis, of the Special Issue of the Springer journal Set-Valued and Variational Analysis in occasion of his 70th anniversary (Volume 30, No. 4, December 2022). He has published more than 150 research papers, but he is better known by his monographs Linear Semi-Infinite Optimization (J. Wiley, 1998), Post-Optimal Analysis in Linear Semi-Infinite Optimization (Springer, 2014) and Even Convexity and Optimization (Springer, 2020), and by his textbooks Algebra and Fundamentals (Ariel, 2000, in Spanish), LinearOptimization (McGraw-Hill, 2004, in Spanish) and Nonlinear Optimization (Springer, 2019). He has also published numerous articles on mathematics and/or politics, history of mathematics, education, etc. He has been Editor-in-Chief of the operations research Springer journal TOP between 2013 and 2016.

Klappentext

Post-Optimal Analysis in Linear Semi-Infinite Optimization examines the following topics in regards to linear semi-infinite optimization: modeling uncertainty, qualitative stability analysis, quantitative stability analysis and sensitivity analysis. Linear semi-infinite optimization (LSIO) deals with linear optimization problems where the dimension of the decision space or the number of constraints is infinite. The authors compare the post-optimal analysis with alternative approaches to uncertain LSIO problems and provide readers with criteria to choose the best way to model a given uncertain LSIO problem depending on the nature and quality of the data along with the available software. This work also contains open problems which readers will find intriguing a challenging. Post-Optimal Analysis in Linear Semi-Infinite Optimization is aimed toward researchers, graduate and post-graduate students of mathematics interested in optimization, parametric optimization and related topics.

Inhalt

1. Preliminaries on Linear Semi-Infinite Optimization.- 2. Modeling uncertain Linear Semi-Infinite Optimization problems.- 3. Robust Linear Semi-infinite Optimization.- 4. Sensitivity analysis.- 5. Qualitative stability analysis.- 6. Quantitative stability analysis.