This book discusses basic tools of partially ordered spaces and applies them to variational methods in Nonlinear Analysis and for optimizing problems. This book is aimed at graduate students and research mathematicians.

Tools in partially ordered spaces are applied to variational methods in nonlinear analysis & optimization theory Developments on vector equilibrium problems; asymptotic behavior of associated Cauchy-type dynamical systems Approaches to robustness & stochastic programming in scalar optimization under uncertainty are derived

Autorentext

Professor Alfred Göpfert researched and taught at the University of Leipzig, at the Technical University of Leuna-Merseburg and at Martin-Luther-University Halle-Wittenberg (Germany). In 1973, his book "Mathematische Optimierung in allgemeinen Vektorräumen" was published by Teubner. Alfred Göpfert has co-authored the textbooks "Funktionalanalysis" (Teubner, 4th edition 1994) and "Lexikon der Optimierung - Optimierung und optimale Steuerung" (Akademie Verlag Berlin, 1986) as well as the monographs "Vektoroptimierung - Theorie, Verfahren und Anwendungen" (Teubner, 1990) and "Variational Methods in Partially Ordered Spaces" (Springer, 2003). Alfred Göpfert worked on the final version of the second edition of the monograph "Variational Methods in Partially Ordered Spaces" until his death in January 2023. Hassan Riahi received his Ph.D. degree in Applied Mathematics in 1989 at the University of Montpelier. Since 1990 he is a Professor in Applied Mathematics at the Sémlalia Faculty of Sciences at the University Cadi Ayyad in Marrakesh. His main research interests include Numerical and theoretical optimization, Variational inequalities, and Convex analysis, and he is the author of over 60 published papers and four edited books. He supervised a dozen doctoral students. Christiane Tammer is Professor at Martin-Luther-University Halle-Witten[1]berg. She is working in the fields of variational analysis and optimization. She has co-authored five monographs, i.e., "Scalarization and Separation by Translation Invariant Functions", Springer (2020); "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 Editor-in-Chief of the journal Optimization, Co-Editor in Chief of the journal Applied Set-Valued Analysis and 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. Constantin Z linescu is a Professor Emeritus (Mathematics) at Alexandru Ioan Cuza University, Iäsi, Romania, and presently he is a Researcher at Octav Mayer Institute of Mathematics, Iäsi, Romania. His research interest is mainly in convex and vector optimization. He (co-)authored four books and more than 100 peer-reviewed journal articles. He has supervised 2 PhD students.

Inhalt
Examples.- Functional Analysis over Cones.- Optimization in Partially Ordered Spaces.- Applications.