Variable Ordering Structures in Vector Optimization

Online-Ressource (XIII, 190 p. 41 illus, online resource)

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Preface; Contents; Chapter1 Variable Ordering Structures; 1.1 Partial Orderings and Variable Ordering Structures; 1.2 Variable Ordering Structures Given by Bishop-Phelps Cones; 1.2.1 Bishop-Phelps Cones; 1.2.2 Augmented Dual Cones; 1.2.3 Variable Ordering Structures Given by Bishop-Phelps Cones; 1.3 Variable Ordering Structures in Applications; 1.3.1 Variable Ordering Structures in Medical Image Registration; 1.3.2 Variable Ordering Structures and Equitability; 1.4 Notes on the Literature; Chapter2 Optimality Concepts and Their Characterization

2.1 Optimality Concepts in Partially Ordered Spaces2.2 Optimality Concepts for Variable Ordering Structures; 2.3 Characterization of Nondominated Elements; 2.4 Characterization of Minimal Elements; 2.5 Notes on the Literature; Chapter3 Cone-Valued Maps; 3.1 Convexity and Linearity of Cone-Valued Maps; 3.1.1 Cone-Convex Cone-Valued Maps; 3.1.2 Convex-Like and Quasiconvex Cone-Valued Maps; 3.1.3 Linear Cone-Valued Maps; 3.1.4 Sublinear Cone-Valued Maps; 3.2 Continuity of Cone-Valued Maps; 3.2.1 Semicontinuous Cone-Valued Maps; 3.2.2 Lipschitz Continuous Cone-Valued Maps

3.3 Monotonicity of Cone-Valued Maps3.4 Notes on the Literature; Chapter4 Linear Scalarizations; 4.1 Characterization of Nondominated Elements; 4.2 Characterization of Minimal Elements; 4.3 Notes on the Literature; Chapter5 Nonlinear Scalarizations; 5.1 Signed Distance Functional; 5.1.1 Characterization of Nondominated Elements; 5.1.2 Characterization of Minimal Elements; 5.2 Translative Functional; 5.2.1 Characterization of Nondominated Elements; 5.2.2 Characterization of Minimal Elements; 5.3 Notes on the Literature

Chapter6 Scalarizations for Variable Orderings Given by Bishop-Phelps Cones6.1 Characterization of Nondominated Elements; 6.2 Characterization of Minimal Elements; 6.3 Notes on the Literature; Chapter7 Optimality Conditions for Vector Optimization Problems; 7.1 Subdifferential and Coderivative; 7.2 Unconstrained Vector Optimization Problems; 7.3 Constrained Vector Optimization Problems; 7.4 Notes on the Literature; Chapter8 Duality Results; 8.1 General Duality; 8.2 Duality Based on Linear Scalarization; 8.3 Duality Based on Nonlinear Scalarization; 8.4 Notes on the Literature

Chapter9 Numerical Methods9.1 Discrete Problems; 9.1.1 Determining Nondominated Elements; 9.1.2 Determining Minimal Elements; 9.2 Continuous Problems; 9.2.1 Determining Nondominated Elements; 9.2.2 Determining Minimal Elements; 9.3 Notes on the Literature; Chapter10 Outlook and Further Application Areas; 10.1 Vector Variational Inequalities and Related Problems; 10.2 Theory of Consumer Demand in Economics; 10.3 Variable Preferences in Intensity-Modulated Radiation Therapy; References; Index

10.1007/978-3-642-54283-1 [DOI]

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