| Document Type
|
:
|
BL
|
| Record Number
|
:
|
890062
|
| Main Entry
|
:
|
Yang, Xinmin.
|
| Title & Author
|
:
|
Generalized preinvexity and second order duality in multiobjective programming /\ Xinmin Yang.
|
| Publication Statement
|
:
|
Singapore :: Springer,, 2018.
|
| Series Statement
|
:
|
Springer optimization and its applications,; volume 142
|
| Page. NO
|
:
|
1 online resource
|
| ISBN
|
:
|
9789811319815
|
|
|
:
|
: 9789811319822
|
|
|
:
|
: 9811319812
|
|
|
:
|
: 9811319820
|
|
|
:
|
9789811319808
|
|
|
:
|
9811319804
|
| Bibliographies/Indexes
|
:
|
Includes bibliographical references and index.
|
| Contents
|
:
|
Intro; Generalized Preinvexity and Second Order Duality in Multiobjective Programming; Abstract; Preface; Contents; Part I Generalized Preinvexity; 1 Preinvex Functions; 1.1 Introduction; 1.2 Notations; 1.3 Semicontinuity and Preinvex Functions; 1.4 Characterizations of Preinvex Functions; 2 Semistrictly Preinvex Functions; 2.1 Introduction and Notations; 2.2 Properties of Semistrictly Preinvex Functions; 2.3 Relationship Between Preinvexity and Semistrict Preinvexity; 2.4 Lower Semicontinuity and Semistrict Preinvexity; 2.5 Gradient Properties of Strictly and Semistrictly Preinvex Functions.
|
|
|
:
|
3 Semipreinvex Functions3.1 Introduction; 3.2 Some New Properties of Semipreinvex Functions; 3.3 Applications to Multiobjective Fractional Programming; 4 Prequasiinvex Functions; 4.1 Introduction and Preliminaries; 4.2 Properties of Prequasiinvex Functions; 4.3 Properties of Semistrictly Prequasiinvex Functions; 4.4 Properties of Strictly Prequasiinvex Functions; 4.5 Applications of Prequasiinvex Type Functions; Part II Generalized Invariant Monotonicity; 5 Generalized Invexity and Generalized Invariant Monotonicity; 5.1 Introduction.
|
|
|
:
|
5.2 Invariant Monotone and Strictly Invariant Monotone Maps5.3 Invariant Quasimonotone Maps; 5.4 Invariant Pseudomonotone Maps; 5.5 Strictly Invariant Pseudomonotone Maps; 5.6 Conclusions; Part III Duality in Multiobjective Programming; 6 Multiobjective Wolfe Type Second-Order Symmetric Duality; 6.1 Introduction; 6.2 Notations and Definitions; 6.3 Wolfe Type I Symmetric Duality; 6.4 Wolfe Type II Symmetric Duality; 7 Multiobjective Mond-Weir-Type Second-Order Symmetric Duality; 7.1 Introduction; 7.2 Notations and Preliminaries; 7.3 Mond-Weir-Type Symmetric Duality; 7.4 Remarks and Examples.
|
|
|
:
|
8 Multiobjective Second-Order Duality with Cone Con\straints8.1 Introduction; 8.2 Preliminaries; 8.3 Weak Duality; 8.4 Strong Duality; 8.5 Converse Duality; 9 Multiobjective Higher-Order Duality; 9.1 Introduction; 9.2 Mond-Weir Type Converse Duality Involving Cone Constraints; 9.3 Mond-Weir Type Symmetric Duality; 9.4 Special Cases; References; Index.
|
| Abstract
|
:
|
This book introduces readers to several new generalized preinvex functions and generalized invariant monotone functions. It begins by describing the main properties of these functions and various relations. Several examples are then presented to illustrate various interesting relationships among preinvex functions and the properly inclusive relations among the generalized invariant monotonicities. In addition, several second order and higher order symmetric duality models are provided for multi-objective nonlinear programming problems. Lastly, weak and strong duality theorems under generalized convexity assumptions are provided. The book offers a well-synthesized, accessible, and usable treatment for students, researchers and practitioners in the areas of OR, optimization, applied mathematics and engineering, and all those working on a wide range of related problems, which include financial institutions, logistics, transportation, traffic management, etc.--
|
| Subject
|
:
|
Mathematical optimization.
|
| Subject
|
:
|
Nonlinear programming.
|
| Subject
|
:
|
Theory of distributions (Functional analysis)
|
| Subject
|
:
|
Mathematical optimization.
|
| Subject
|
:
|
MATHEMATICS-- Calculus.
|
| Subject
|
:
|
MATHEMATICS-- Mathematical Analysis.
|
| Subject
|
:
|
Nonlinear programming.
|
| Subject
|
:
|
Theory of distributions (Functional analysis)
|
| Dewey Classification
|
:
|
515/.782
|
| LC Classification
|
:
|
QA324
|