Multi-dimensional Control Problems

This book deals with several types of multi-dimensional control problems in the face of data uncertainty for vector casesmulti-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 approachesan exact l1 penalty function approach, modified objective approach, robust approachin the simplest way to solve the recent developing optimization problems in the sense of uncertainty.

Discusses variational control problems involving first- and second-order PDE and PDI constraints Presents novel approaches to handle the uncertainty in multi-objective optimization problems Focuses on benefits of the multi-dimensional problem over finite and infinite restrictions

Auteur
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.

Résumé
"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)

Contenu
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. <p