دانلود کتاب Variational Analysis and Set Optimization-Developments and Applications in Decision Making

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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

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

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

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

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