Variational Analysis and Set Optimization: Developments and Applications in Decision Making

ISBN-13: 9781138037267 / Angielski / Twarda / 2019 / 336 str.

Akhtar A. Khan; Elisabeth Kobis; Christiane Tammer

Opis

This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control, and bilevel optimization. In addition, recent developments concerning scalarization techniques, necessary and sufficient optimality conditions and duality statements are discussed. These new numerical methods help practitioners efficiently solve set optimization problems in real-world situations. Moreover, applications in economics, finance and risk theory are discussed. These simple techniques are designed to help practitioners in the decision-making process, as well as to give an overview of nondominated solutions to choose from.

Spis treści

Advances in Set-valued and Variational Analysis and Optimization Theory. Metric Regularity. Solution Concepts in Set Optimization. Vector and Set Optimization with Variable Domination Structure. Applications of Set Optimization to Robustness and Uncertainties. Existence Results for Generalized Variational Inequalities and Applications. Scalarization Techniques in Set Optimization. Necessary and Sufficient Optimality Conditions for Set Optimization Problems. Duality in Set Optimization: An Overview of Existing Approaches and New Advances. Numerical Methods for Solving Set Optimization Problems. Applications of Set Optimization in Economics, Finance and Risk Theory.

O autorze

Akhtar Khan is a Professor at Rochester Institute of Technology. His has published more than seventy papers on set-valued optimization, inverse problems, and variational inequalities. He is a co-author of Set-valued Optimization, Springer (2015),　and Co-editor of Nonlinear Analysis and Variational Problems, Springer (2009). He is Co-Editor in Chief of the Journal of Applied and Numerical Optimization, and Editorial Board member of Optimization, Journal of Optimization Theory and Applications, and Journal of Nonlinear and Variational Analysis.

Elisabeth Köbis is a lecturer and researcher at Martin-Luther-University Halle-Wittenberg, Germany. She received her PhD from Martin-Luther-University Halle-Wittenberg, Germany, in 2014. Her research interests lie in vector and set optimization and its applications to uncertain optimization, in particular robust approaches to uncertain multi-objective optimization problems, and unified approaches to uncertain optimization using nonlinear scalarization, vector variational inequalities and variable domination structures.

Christiane Tammer is working on the field variational analysis and optimization. She has co-authored 4 monographs, i.e. Set-valued Optimization - An Introduction with Applications. Springer (2015), Variational Methods in Partially Ordered Spaces. Springer (2003), Angewandte Funktionalanalysis. Vieweg+Teubner (2009), Approximation und Nichtlineare Optimierung in Praxisaufgaben. Springer (2017). She is the Editor in Chief of the journal Optimization and a member of the Editorial Board of several journals, the Scientific Committee of the Working Group on Generalized Convexity and　EUROPT Managing Board.