Intro
Foreword
Preface
Contents
Contributors
1 Linear and Pascoletti-Serafini Scalarizations in Unified Set Optimization
1.1 Introduction
1.2 Preliminaries
1.3 Scalarization
1.4 Linear Scalarizations
1.5 Pascoletti-Serafini Scalarization Scheme
1.6 Conclusions
References
2 A Gradient-Free Method for Multi-objective Optimization Problem
2.1 Introduction
2.2 Notations and Preliminaries
2.3 Gradient-Free Method for MOP
2.3.1 Modified Nelder-Mead Algorithm
2.4 Numerical Illustrations and Performance Assessment
2.5 Performance Profile

2.6 Conclusions
References
3 The New Butterfly Relaxation Method for Mathematical Programs with Complementarity Constraints
3.1 Introduction
3.2 Preliminaries
3.2.1 Non-Linear Programming
3.2.2 Mathematical Programs with Complementarity Constraints
3.3 The Butterfly Relaxation Method
3.4 Theoretical Properties
3.4.1 Convergence
3.4.2 Existence of Lagrange Multipliers for the Relaxed Sub-Problems
3.4.3 Convergence of the Epsilon-Stationary Points
3.5 Numerical Results
3.5.1 On the Implementation of the Butterfly Relaxation

3.5.2 Comparison of the Relaxation Methods
3.6 Concluding Remarks
Appendix
3.7 Proof of a Technical Lemma
References
4 Copositive Optimization and Its Applications in Graph Theory
4.1 Introduction
4.1.1 Quadratic Programming Problem with Binary and Continuous Variables
4.1.2 Fractional Quadratic Optimization Problem
4.1.3 More on Nonconvex Quadratic Programming Problems
4.1.4 Quadratic Optimization Problem and the Concept of Lifted Problem
4.1.5 Quadratic Optimization Problem and the Role of Special Matrix Classes

6 Set Order Relations, Set Optimization, and Ekeland's Variational Principle
6.1 Introduction
6.2 Preliminaries
6.3 Set Order Relations
6.3.1 Set Order Relations in Terms of the Minkowski Difference
6.3.2 Set Order Relations with Respect to Variable Domination Structures
6.4 Nonlinear Scalarization Functions
6.4.1 Weighted Set Order Relations
6.5 Solution Concepts in Set Optimization
6.5.1 Solution Concepts in Set Optimization with Respect to Variable Domination Structures
6.6 Existence of Solutions
6.6.1 Generalized Semicontinuity for Set-Valued Maps