This book deals with several types of multi-dimensional control problems in the face of data uncertainty for vector cases―multi-dimensional multi-objective control problem with uncertain objective functionals, uncertain constraint functionals, and uncertain objective as well as constraint functionals, uncertain multi-dimensional multi-objective control problem with semi-infinite constraints, uncertain dual multi-dimensional multi-objective variational control problem, and second-order PDE&PDI constrained robust optimization problem. The book provides the solution approaches―an exact l1 penalty function approach, modified objective approach, robust approach―in the simplest way to solve the recent developing optimization problems in the sense of uncertainty.
Author(s): Anurag Jayswal, Preeti, Savin Treanţӑ
Series: Industrial and Applied Mathematics
Publisher: Springer
Year: 2022
Language: English
Pages: 194
City: Singapore
Preface
Contents
About the Authors
Glossary of Notations
1 Introduction
1.1 Overview of Literature
1.2 Pontryagin Maximum Principle for Single-time Optimal Control Problem…
1.3 Pontryagin Maximum Principle for Multi-time Optimal Control Problem…
1.4 General Construction of Multi-dimensional Control Problems
1.5 Classification of the Multi-dimensional Cost Functionals
1.5.1 Curvilinear Integral Cost Functional
1.5.2 Multiple Integral Cost Functional
1.6 Necessary and Sufficient Efficiency Conditions
1.7 Robust Approach
1.8 Penalty Function Method
1.9 Saddle-point Criterion
1.10 Duality Theory
1.10.1 Wolfe Type Dual Problem
1.10.2 Mond-Weir Type Dual Problem
1.10.3 Mixed Type Dual Problem
References
2 Multi-dimensional Variational Control Problem with Data Uncertainty in Objective Functional
2.1 Introduction
2.2 Problem Description
2.3 Robust Sufficient Efficiency Conditions
2.4 The Exact l1 Penalty Function Method
2.5 Uncertain Lagrange Functional
References
3 Multi-dimensional Variational Control Problem with Data Uncertainty in Constraint Functionals
3.1 Introduction
3.2 Problem Description
3.3 Robust Sufficient Efficiency Conditions
3.4 Robust Saddle-point Criteria and Exact l1 Penalty Function Method
References
4 Multi-dimensional Variational Control Problem with Data Uncertainty in Objective and Constraint Functionals
4.1 Introduction
4.2 Problem Description
4.3 Robust Sufficient Efficiency Conditions
4.4 The Exact l1 Penalty Function Method
4.5 Uncertain Lagrange Functional
References
5 The Modified Approach for Multi-dimensional Optimization Problem with Data Uncertainty
5.1 Introduction
5.2 Problem Description
5.3 Modified Multi-dimensional Multi-objective Optimization Problem
5.4 The Exact l1 Penalty Function Method
References
6 Semi-infinite Multi-dimensional Variational Control Problem with Data Uncertainty
6.1 Introduction
6.2 Problem Description
6.3 Robust Sufficient Efficiency Conditions
6.4 The Exact l1 Penalty Function Method
6.5 Uncertain Lagrange Functional
6.6 Robust Saddle-point Criteria
References
7 Robust Duality for Multi-dimensional Variational Control Problem with Data Uncertainty
7.1 Introduction
7.2 Problem Description
7.3 Wolfe Type Robust Duality
7.4 Mond-Weir Type Robust Dual Problem
7.5 Mixed Type Robust Dual Problem
References
8 On a Class of Second-Order PDE&PDI Constrained Robust Optimization Problems
8.1 Introduction
8.2 Problem Description
8.3 Robust Sufficient Efficiency Conditions
8.4 The Associated Modified Optimization Problem
8.5 The Associated Saddle-Point Efficiency Criterion
References
