Buch, Englisch, 510 Seiten, Format (B × H): 155 mm x 229 mm, Gewicht: 816 g
Buch, Englisch, 510 Seiten, Format (B × H): 155 mm x 229 mm, Gewicht: 816 g
ISBN: 978-1-4822-5573-7
Verlag: Taylor & Francis Ltd (Sales)
The book describes the characterizations of solution sets of various optimization problems. It examines multiobjective pseudolinear, multiobjective fractional pseudolinear, static minmax pseudolinear, and static minmax fractional pseudolinear optimization problems and their results. The authors extend these results to locally Lipschitz functions using Clarke subdifferentials. They also present optimality and duality results for h-pseudolinear and semi-infinite pseudolinear optimization problems.
The authors go on to explore the relationships between vector variational inequalities and vector optimization problems involving pseudolinear functions. They present characterizations of solution sets of pseudolinear optimization problems on Riemannian manifolds as well as results on pseudolinearity of quadratic fractional functions. The book also extends n-pseudolinear functions to pseudolinear and n-pseudolinear fuzzy mappings and characterizations of solution sets of pseudolinear fuzzy optimization problems and n-pseudolinear fuzzy optimization problems. The text concludes with some applications of pseudolinear optimization problems to hospital management and economics.
This book encompasses nearly all the published literature on the subject along with new results on semi-infinite nonlinear programming problems. It will be useful to readers from mathematical programming, industrial engineering, and operations management.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Introduction
Convex Sets
Convex Functions and Properties
Alternative and Separation Theorems
Unconstrained and Constrained Optimization Problems
Nonlinear Multiobjective Optimization and Pareto Optimality
Subdifferential Calculus
Optimality Criteria and Duality
Pseudolinear Functions: Characterizations and Properties
Introduction
Differentiable Pseudolinear Functions
Local Characterizations of Pseudolinear Functions
Second Order Characterizations of Pseudolinear Functions
Semilocally Pseudolinear Functions
Dini Derivatives and Pseudolinear Functions
Characterizations of Locally Lipschitz Pseudolinear Functions using Clarke Subdifferential
Weakly Pseudolinear Functions
Properties of the Functional Class of Differentiable at a Point Functions
Constrained Pseudolinear Optimization Problems: Characterizations of Solution Sets
Introduction
Characterizations of Solution Sets of Differentiable Pseudolinear Optimization Problems
Solution Sets of Linear Fractional Programs
Characterizations of Solution Sets of Semilocally Pseudolinear Optimization Problems
Characterizations of Solution Sets of Pseudolinear Optimization Problems in Terms of Dini Derivatives
Characterizations of Solution Sets of h-Pseudolinear Optimization Problems
Characterizations of Solution Sets of Nonsmooth Pseudolinear Optimization Problems
Constrained Pseudolinear Optimization Problems: Characterizations of Solutions Sets in Terms of Lagrange Multipliers
Introduction
Definitions and Preliminaries
Pseudolinear Optimization Problems
Linear Fractional Programming Problem
Vector Linear Fractional Programming Problem
Nonsmooth Pseudolinear Optimization Problems with Linear Inequality Constraints
Nonsmooth Vector Pseudolinear Optimization Problems with Linear Inequality Constraints
Pseudolinearity in terms of Bifunction
Necessary Optimality Conditions for a Mathematical Program in terms of Bifunctions
Mathematical Program with h-Convex Objective and j h-Pseudolinear Constraints
Mathematical Program with h-Pseudolinear Objective and j h-Pseudolinear Constraints
Pseudolinear Multiobjective Optimization
Introduction
Necessary Optimality Conditions
Sufficient Optimality Conditions
Duality in Multiobjective Programming
Multiobjective Fractional Programming Problems
Necessary Optimality Conditions
Sufficient Optimality Conditions
Duality in Multiobjective Fractional Programming
Nonsmooth Pseudolinear Multiobjective Optimization
Introduction
Necessary Optimality Conditions
Sufficient Optimality Conditions
Duality Theorems
Nonsmooth Multiobjective Fractional Programming
Necessary Optimality Conditions
Sufficient Optimality Conditions
Duality Theorems
Static Minimax Programming and Pseudolinear Functions
Minimax Programming Problems
Necessary Optimality Conditions
Sufficient Optimality Conditions
Duality for Minimax Programming Problem
Minimax Fractional Programming Problem
Necessary Optimality Conditions
Sufficient Optimality Conditions
Duality for Minimax Fractional Programming
Nonsmooth Static Minimax Programming and Pseudolinear Functions
Introduction
Definitions and Preliminaries
Necessary and Sufficient Optimality Conditions
Dual Model I
Dual Model II
Nonsmooth Multiobjective Pseudolinear Programming: Optimality and Duality in Terms of Bifunctions
Introduction
Definitions and Preliminaries
Necessary and Sufficient Optimality Conditions
Duality Theorem
Numerical Examples
Pseudolinear Multiobjective Semi-Infinite Programming Problems
Introduction
Necessary and Sufficient Optimality Conditions
Duality Theorems
Nonsmooth Semi-infinite Programming Problems
Necessary and Sufficient Optimality Conditions
Duality Theorems
Numerical Examples
Vector Variational Inequality and Vector Pseudolinear Optimization Problems
Introduction
Vector Variational Inequality Problems
Necessary and Sufficient Optimality Conditions
Nonsmooth Vector Variational Inequality Problems
Necessary and Sufficient Optimality Conditions
Extension of Pseudolinear Functions and Variational Inequality Problems
Introduction
PPM maps and their Characterizations
Affine PPM Maps
Characterizations of the Solutio
