Mishra / Upadhyay Pseudolinear Functions and Optimization

Erscheinungsjahr 2015
ISBN: 978-1-4822-5575-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 510 Seiten

This is the first book to focus exclusively on pseudolinear functions, a class of generalized convex functions. It discusses the properties, characterizations, and applications of pseudolinear functions in nonlinear optimization problems, providing numerous examples from everyday life that aid readers in understanding key concepts and results. Encompassing nearly all the related literature published from 1965 to 2013, as well as some new results on semi-infinite nonlinear programming problems, the text is useful to research scholars and practitioners in mathematical programming, industrial engineering, and operations management.

Autoren/Hrsg.

Mishra, Shashi Kant

Upadhyay, Balendu Bhooshan

Fachgebiete

• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung

Inhaltsverzeichnis

List of Figures

Notations

Preface

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 Progr