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Set-valued optimization : an introduction with applications /
Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between certain spaces. Since set-valued maps subsumes single valued maps, set-valued optimization provides an...
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| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin :
Springer,
[2015]
|
| Series: | Vector optimization.
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| Subjects: | |
| Online Access: |
Full text (Wentworth users only) |
| Local Note: | ProQuest Ebook Central |
MARC
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| 100 | 1 | |a Khan, Akhtar A., |e author. | |
| 245 | 1 | 0 | |a Set-valued optimization : |b an introduction with applications / |c Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu. |
| 264 | 1 | |a Berlin : |b Springer, |c [2015] | |
| 300 | |a 1 online resource (xxii, 765 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |b PDF | ||
| 347 | |a text file | ||
| 490 | 1 | |a Vector Optimization, |x 1867-8971 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |6 880-01 |a Introduction -- Order Relations and Ordering Cones -- Continuity and Differentiability -- Tangent Cones and Tangent Sets -- Nonconvex Separation Theorems -- Hahn-Banach Type Theorems -- Hahn-Banach Type Theorems -- Conjugates and Subdifferentials -- Duality -- Existence Results for Minimal Points -- Ekeland Variational Principle -- Derivatives and Epiderivatives of Set-valued Maps -- Optimality Conditions in Set-valued Optimization -- Sensitivity Analysis in Set-valued Optimization and Vector Variational Inequalities -- Numerical Methods for Solving Set-valued Optimization Problems -- Applications. | |
| 520 | |a Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between certain spaces. Since set-valued maps subsumes single valued maps, set-valued optimization provides an important extension and unification of the scalar as well as the vector optimization problems. Therefore this relatively new discipline has justifiably attracted a great deal of attention in recent years. This book presents, in a unified framework, basic properties on ordering relations, solution concepts for set-valued optimization problems, a detailed description of convex set-valued maps, most recent developments in separation theorems, scalarization techniques, variational principles, tangent cones of first and higher order, sub-differential of set-valued maps, generalized derivatives of set-valued maps, sensitivity analysis, optimality conditions, duality, and applications in economics among other things. | ||
| 546 | |a English. | ||
| 588 | 0 | |a Online resource; title from PDF title page (EBSCO, viewed November 10, 2014). | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Duality theory (Mathematics) | |
| 650 | 0 | |a Mathematical optimization. | |
| 650 | 0 | |a Set-valued maps. | |
| 650 | 0 | |a Programming (Mathematics) | |
| 650 | 0 | |a Search theory. | |
| 650 | 0 | |a Mathematics. | |
| 650 | 2 | 2 | |a Decision Theory |
| 650 | 2 | |a Mathematics | |
| 650 | 7 | |a applied mathematics. |2 aat | |
| 650 | 7 | |a mathematics. |2 aat | |
| 700 | 1 | |a Tammer, Christiane, |e author. | |
| 700 | 1 | |a Zălinescu, Constantin, |e author. | |
| 758 | |i has work: |a Set-valued optimization (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGQG43RWMR4GMRfjkxFPHC |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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| 776 | 0 | 8 | |i Printed edition: |z 9783642542640 |
| 830 | 0 | |a Vector optimization. | |
| 852 | |b Ebooks |h ProQuest | ||
| 856 | 4 | 0 | |u https://ebookcentral.proquest.com/lib/wit/detail.action?docID=1968316 |z Full text (Wentworth users only) |t 0 |
| 880 | 0 | 0 | |6 505-01/(S |t Pavel -- |g 4.15.4. |t Connections Among the Second-Order Tangent Cones -- |g 4.16. |t Second-Order Local Approximation -- |g 4.17. |t Higher-Order Tangent Cones and Tangent Sets -- |g 5.1. |t Separating Functions and Examples -- |g 5.2. |t Nonlinear Separation -- |g 5.2.1. |t Construction of Scalarizing Functionals -- |g 5.2.2. |t Properties of Scalarization Functions -- |g 5.2.3. |t Continuity Properties -- |g 5.2.4. |t Lipschitz Properties -- |g 5.2.5. |t Formula for the Conjugate and Subdifferential of φA for A Convex -- |g 5.3. |t Scalarizing Functionals by Hiriart-Urruty and Zaffaroni -- |g 5.4. |t Characterization of Solutions of Set-Valued Optimization Problems by Means of Nonlinear Scalarizing Functionals -- |g 5.4.1. |t Extension of the Functional cpA -- |g 5.4.2. |t Characterization of Solutions of Set-Valued Optimization Problems with Lower Set Less Order Relation> or = to C by Scalarization -- |g 5.5. |t Extremal Principle -- |g 6.1. |t Hahn-Banach-Kantorovich Theorem -- |g 6.2. |t Classical Separation Theorems for Convex Sets -- |g 6.3. |t Core Convex Topology -- |g 6.4. |t Yang's Generalization of the Hahn-Banach Theorem -- |g 6.5. |t Sufficient Condition for the Convexity of R+A -- |g 7.1. |t Strong Conjugate and Subdifferential -- |g 7.2. |t Weak Subdifferential -- |g 7.3. |t Subdifferentials Corresponding to Henig Proper Efficiency -- |g 7.4. |t Exact Formulas for the Subdifferential of the Sum and the Composition -- |g 8.1. |t Duality Assertions for Set-Valued Problems Based on Vector Approach -- |g 8.1.1. |t Conjugate Duality for Set-Valued Problems Based on Vector Approach -- |g 8.1.2. |t Lagrange Duality for Set-Valued Optimization Problems Based on Vector Approach -- |g 8.2. |t Duality Assertions for Set-Valued Problems Based on Set Approach -- |g 8.3. |t Duality Assertions for Set-Valued Problems Based on Lattice Structure -- |g 8.3.1. |t Conjugate Duality for F-Valued Problems -- |g 8.3.2. |t Lagrange Duality for F-Valued Problems -- |g 8.4. |t Comparison of Different Approaches to Duality in Set-Valued Optimization -- |g 8.4.1. |t Lagrange Duality -- |g 8.4.2. |t Subdifferentials and Stability -- |g 8.4.3. |t Duality Statements with Operators as Dual Variables -- |g 9.1. |t Preliminary Notions and Results Concerning Transitive Relations -- |g 9.2. |t Existence of Minimal Elements with Respect to Transitive Relations -- |g 9.3. |t Existence of Minimal Points with Respect to Cones -- |g 9.4. |t Types of Convex Cones and Compactness with Respect to Cones -- |g 9.5. |t Existence of Optimal Solutions for Vector and Set Optimization Problems -- |g 10.1. |t Preliminary Notions and Results -- |g 10.2. |t Minimal Points in Product Spaces -- |g 10.3. |t Minimal Points in Product Spaces of Isac-Tammer's Type -- |g 10.4. |t Ekeland's Variational Principles of Ha's Type -- |g 10.5. |t Ekeland's Variational Principle for Bi-Set-Valued Maps -- |g 10.6. |t EVP Type Results -- |g 10.7. |t Error Bounds -- |g 11.1. |t Contingent Derivatives of Set-Valued Maps -- |g 11.1.1. |t Miscellaneous Graphical Derivatives of Set-valued Maps -- |g 11.1.2. |t Convexity Characterization Using Contingent Derivatives -- |g 11.1.3. |t Proto-Differentiability, Semi-Differentiability, and Related Concepts -- |g 11.1.4. |t Weak Contingent Derivatives of Set-Valued Maps -- |g 11.1.5. |t Lyusternik-Type Theorem Using Contingent Derivatives -- |g 11.2. |t Calculus Rules for Derivatives of Set-Valued Maps -- |g 11.2.1. |t Calculus Rules by a Direct Approach -- |g 11.2.2. |t Derivative Rules by Using Calculus of Tangent Cones -- |g 11.3. |t Contingently C -Absorbing Maps -- |g 11.4. |t Epiderivatives of Set-Valued Maps -- |g 11.4.1. |t Contingent Epiderivatives of Set-Valued Maps with Images in R -- |g 11.4.2. |t Contingent Epiderivatives in General Spaces -- |g 11.4.3. |t Existence Theorems for Contingent Epiderivatives -- |g 11.4.4. |t Variational Characterization of the Contingent Epiderivatives -- |g 11.5. |t Generalized Contingent Epiderivatives of Set-Valued Maps -- |g 11.5.1. |t Existence Theorems for Generalized Contingent Epiderivatives -- |g 11.5.2. |t Characterizations of Generalized Contingent Epiderivatives -- |g 11.6. |t Calculus Rules for Contingent Epiderivatives -- |g 11.7. |t Second-Order Derivatives of Set-Valued Maps -- |g 11.8. |t Calculus Rules for Second-Order Contingent Derivatives -- |g 11.9. |t Second-Order Epiderivatives of Set-Valued Maps -- |g 12.1. |t First-Order Optimality Conditions by the Direct Approach -- |g 12.2. |t First-Order Optimality Conditions by the Dubovitskii-Milyutin Approach -- |g 12.2.1. |t Necessary Optimality Conditions by the Dubovitskii-Milyutin Approach -- |g 12.2.2. |t Inverse Images and Subgradients of Set-Valued Maps -- |g 12.2.3. |t Separation Theorems and the Dubovitskii-Milyutin Lemma -- |g 12.2.4. |t Lagrange Multiplier Rules by the Dubovitskii-Milyutin Approach -- |g 12.3. |t Sufficient Optimality Conditions in Set-Valued Optimization -- |g 12.3.1. |t Sufficient Optimality Conditions Under Convexity and Quasi-Convexity -- |g 12.3.2. |t Sufficient Optimality Conditions Under Paraconvexity -- |g 12.3.3. |t Sufficient Optimality Conditions Under Semidifferentiability -- |g 12.4. |t Second-Order Optimality Conditions in Set-Valued Optimization -- |g 12.4.1. |t Second-Order Optimality Conditions by the Dubovitskii-Milyutin Approach -- |g 12.4.2. |t Second-Order Optimality Conditions by the Direct Approach -- |g 12.5. |t Generalized Dubovitskii-Milyutin Approach in Set-Valued Optimization -- |g 12.5.1. |t Separation Theorem for Multiple Closed and Open Cones -- |g 12.5.2. |t First-Order Generalized Dubovitskii-Milyutin Approach -- |g 12.5.3. |t Second-Order Generalized Dubovitskii-Milyutin Approach -- |g 12.6. |t Set-Valued Optimization Problems with a Variable Order Structure -- |g 12.7. |t Optimality Conditions for Q-Minimizers in Set-Valued Optimization -- |g 12.7.1. |t Optimality Conditions for Q-Minimizers Using Radial Derivatives -- |g 12.7.2. |t Optimality Conditions for Q-Minimizers Using Coderivatives -- |g 12.8. |t Lagrange Multiplier Rules Based on Limiting Subdifferential -- |g 12.9. |t Necessary Conditions for Approximate Solutions of Set-Valued Optimization Problems -- |g 12.10. |t Necessary and Sufficient Conditions for Solution Concepts Based on Set Approach -- |g 12.11. |t Necessary Conditions for Solution Concepts with Respect to a General Preference Relation -- |g 12.12. |t KKT-Points and Corresponding Stability Results -- |g 13.1. |t First Order Sensitivity Analysis in Set-Valued Optimization -- |g 13.2. |t Second Order Sensitivity Analysis in Set-Valued Optimization -- |g 13.3. |t Sensitivity Analysis in Set-Valued Optimization Using Coderivatives -- |g 13.4. |t Sensitivity Analysis for Vector Variational Inequalities. |
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