Multi-dimensional Control Problems

Robust Approach

Anurag Jayswal, Preeti, Savin Treanţӑ

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English

Springer Verlag, Singapore
02 November 2023

Cybernetics & systems theory; Optimisation; Applied mathematics; Mathematical modelling; Maths for engineers

Series: Industrial and Applied Mathematics

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.

By: Anurag Jayswal, Preeti, Savin Treanţӑ
Imprint: Springer Verlag, Singapore
Country of Publication: Singapore
Edition: 2022 ed.
Dimensions: Height: 235mm, Width: 155mm,
Weight: 320g
ISBN: 9789811965630
ISBN 10: 9811965633
Series: Industrial and Applied Mathematics
Pages: 186
Publication Date: 02 November 2023
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Preface.- Glossary of Notations.- Chapter 1. Introduction.- Chapter 2. Multi-dimensional Variational Control Problem with Data Uncertainty in Objective Functional.- Chapter 3. Multi-dimensional Variational Control Problem with Data Uncertainty in Constraint Functionals.- Chapter 4. Multi-dimensional Variational Control Problem with Data Uncertainty in Objective and Constraint Functionals.- Chapter 5. The Modified Approach for Multi-dimensional Optimization Problem with Data Uncertainty.- Chapter 6. Semi-infinite Multi-dimensional Variational Control Problem with Data Uncertainty.- Chapter 7. Robust Duality for Multi-dimensional Variational Control Problem with Data Uncertainty.- Chapter 8. On a Class of Second-order PDE&PDI Constrained Robust Optimization Problems.- Bibliography.

ANURAG JAYSWAL is an associate professor at the Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines) Dhanbad, India. He earned his Ph.D. degree in mathematics from Banaras Hindu University, Varanasi, India. He obtained his master in mathematics from same university and was awarded first order of merit. He received a young scientist project from the Department of Science and Technology, Government of India. He has more than 15 years of teaching experience at Birla Institute of Technology (BIT) Mesra, Ranchi, India, and IIT (ISM) Dhanbad, India. His research interest is in continuous optimization, nonsmooth optimization, generalized convexity, control theory, and variational inequalities problems. He is the author and coauthor of more than 100 research papers in the field of continuous optimization and variational inequalities and has supervised more than 10 Ph.D. students. He is on the editorial board of OPSEARCH and Advancesin Variational Inequalities. He visited several countries to deliver their talks in international conferences. He is a reviewer of various international journals. PREETI is an assistant professor at the Department of Applied Science and Humanities, Inderprastha Engineering College, Ghaziabad, India. She completed her Ph.D. degree in mathematics from the Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines) Dhanbad, India. Her research interest is in multi-time optimization problem, generalized convexity, and control theory. She has published many scientific papers on these topics in various prominent journals. SAVIN TREANTA is a lecturer at the Department of Applied Mathematics, Faculty of Applied Sciences, University Politehnica of Bucharest, Romania. His research interests include optimization theory, control theory, nonlinear and variational analysis, geometric partial differential equations, and information theory. He haspublished more than 80 scientific papers on these topics in various prestigious journals.

Reviews for Multi-dimensional Control Problems: Robust Approach

“The book contains eight chapters, each of them ending with a list of references. … the authors present a complete analysis of multi-dimensional and multi-objective variational control problems, also in the case of data uncertainty. The different definitions and results are illustrated with examples.” (Alain Brillard, zbMATH 1514.49001, 2023)