Variational analysis and set optimization : developments and applications in decision making /: developments and applications in decision making. (2019)

• Record Type: Book
• Further Information: Note: Akhtar A. Khan (Center for Applied and Computational Mathematics, School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY, USA), Elisabeth Köbis (Institute of Mathematics, Martin-Luther-University, Halle-Wittenberg, Faculty of Natural Sciences II, Halle, Germany), Christiane Tammer (Institute of Mathematics, Martin-Luther-University Halle-Wittenberg, Halle, Germany).
• Authors: Khan, Akhtar A; Köbis, Elisabeth; Tammer, Christiane
• Contents: Preface Variational Analysis and Variational Rationality in Behavioral Sciences Boris S. Mordukhovich and Antoine Soubeyran Introduction Variational Rationality in Behavioral Sciences Evaluation Aspects of Variational Rationality Exact Stationary Traps in Behavioral Dynamics Evaluations of Approximate Stationary Traps Geometric Evaluations and Extremal Principle Summary of Major Finding and Future Research References A Financial Model for a Multi-Period Portfolio Optimization Problem Gabriella Colajanni and Patrizia Daniele Introduction The Financial Model Variational Inequality Formulation and Existence Results Numerical Examples Conclusions References A Generalized Proximal Alternating Linearized Method Antoine Soubeyran, Jo˜ao Carlos Souza, and Jo˜ao Xavier Cruz Neto Introduction Potential Games: How to Play Nash? Variational Analysis: How to Optimize a Potential Function? Variational Rationality: How Human Dynamics Work? Computing How to Play Nash for Potential Games References Sublinear-like Scalarization Scheme for Sets and its Applications Koichiro Ike, Yuto Ogata, Tamaki Tanaka, and Hui Yu Introduction Set Relations and Scalarizing Functions for Sets Inherited Properties of Scalarizing Functions Applications to Set-valued Inequality and Fuzzy Theory References Functions with Uniform Sublevel Sets, Epigraphs and Continuity Petra Weidner Introduction Preliminaries Directional Closedness of Sets Definition of Functions with Uniform Sublevel Sets Translative Functions Nontranslative Functions with Uniform Sublevel Sets Extension of Arbitrary Functionals to Translative Functions References Optimality and Viability Conditions for State-Constrained Control Problems Robert Kipka Introduction Background Strict Normality and the Decrease Condition Metric Regularity, Viability, and the Maximum Principle Closing Remarks References Lipschitz Properties of Cone-convex Set-valued Functions Vu Anh Tuan and Thanh Tam Le Introduction Preliminaries Concepts on Convexity and Lipschitzianity of Set-valued Functions Lipschitz Properties of Cone-convex Set-valued Functions Conclusions References Vector Optimization with Variable Ordering Structures Marius Durea, Elena-Andreea Florea, and Radu Strugariu Introduction Preliminaries Efficiency Concepts Sufficient Conditions for Mixed Openness Necessary Optimality Conditions Bibliographic Notes, Comments, and Conclusions References Vectorial Penalization in Multi-objective Optimization Christian G¨unther Introduction Preliminaries in Generalized Convex Multi-objective Optimization Pareto Efficiency with Respect to Different Constraint Sets A Vectorial Penalization Approach in Multi-objective Optimization Penalization in Multi-objective Optimization with Functional Conclusions References Set Optimization Problems Reducible to Vector Optimization Problems Gabriele Eichfelder and Tobias Gerlach Introduction Basics of Vector and Set Optimization Set Optimization Problems Being Reducible to Vector Optimization Problems Implication on Set-valued Test Instances References Abstract Convexity and Solvability Theorems Ali Reza Doagooei Introduction Abstract Convex Functions Solvability Theorems for Real-valued Systems of Inequalities Vector-valued Abstract Convex Functions and Solvability Theorems Applications in Optimization References Regularization Methods for Scalar and Vector Control Problems Baasansuren Jadamba, Akhtar A. Khan, Miguel Sama, and Christiane Tammer Introduction Lavrentiev Regularization Conical Regularization Half-space Regularization Integral Constraint Regularization A Constructible Dilating Regularization Regularization of Vector Optimization Problems Concluding Remarks and Future Research References
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2019
• Extent: 1 online resource
• Subjects: 515/.64; Calculus of variations; Mathematical analysis; Variational inequalities (Mathematics); Mathematical optimization; MATHEMATICS / Calculus; MATHEMATICS / Mathematical Analysis; Electronic books
• Languages: English
• ISBNs: 9781315177991; 1315177994; 9781351712064; 1351712063
• Related ISBNs: 1138037265; 9781138037267
• Notes: Note: Includes bibliographical references and index.
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