Unconstrained Optimization and Quantum Calculus

This book provides a better clue to apply quantum derivative instead of classical derivative in the modified optimization methods, compared with the competing books which employ a number of standard derivative optimization techniques to address large-scale, unconstrained optimization issues. Essential proofs and applications of the various techniques are given in simple manner without sacrificing accuracy. New concepts are illustrated with the help of examples. This book presents the theory and application of given optimization techniques in generalized and comprehensive manner. Methods such as steepest descent, conjugate gradient and BFGS are generalized and comparative analyses will show the efficiency of the techniques.

Gives an exhaustive review of the literature Presents introduction of quantum calculus in the optimization methods Covers all classical optimization methods which are generalized for improving the results

Auteur

Bhagwat Ram is a Post-Doctoral Research Associate at the Centre for Digital Transformation at the Indian Institute of Management Ahmedabad, India. He received his Ph.D. from DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science at the Banaras Hindu University, Varanasi, India (#21). His research interests include numerical optimization, digital innovation and transformation, supply chain management, and complex networks. He has six years of teaching and eight years of research experience. He has published 20 research articles in the science citation index and expanded listed journals. He has co-authored two books: Introduction to Linear Programming with MATLAB*, and Introduction to Unconstrained Optimization with R *with Prof. Shashi Kant Mishra. His research has been published in journals such as Frontiers in Public Health, Journal of Applied Mathematics and Computing, Yugoslav Journal of Operations Research, Mathematics, AIMS Mathematics, Advances in Difference Equations, Journal of Inequalities and Applications, Nonlinear Dynamics, Pacific Journal of Optimization, Journal of Marine Science & Engineering, Fractal and Fractional, Processes, and Energies.

Shashi Kant Mishra, Ph.D., D.Sc., is a Professor at the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India. With over 25 years of teaching experience, he has authored nine books, including textbooks and monographs, and has been on the editorial boards of several respected international journals. He has guest-edited special issues of the Journal of Global Optimization and Optimization Letters (both Springer Nature) and Optimization (Taylor & Francis). A DST Fast Track Fellow (2001-2002) and INSA Teacher Award (2020-21) Prof. Mishra has published over 200 papers and supervised 22 Ph.D. students. He has visited around 16 institutes/universities in countries such as France, Canada, Italy, Spain, Japan, Taiwan, China, Singapore, Vietnam, and Kuwait. He has completed several projects sponsored by BHU, DST, and UGC.

Kin Keung Lai received his Ph.D. degree at Michigan State University in the USA in 1977. He is currently a Professor at the International Business School of Shaanxi Normal University and an Honorary Professor in the Department of Industrial and Manufacturing Systems Engineering at the University of Hong Kong. Prior to his current posts, he was Chair Professor of Management Science at City University of Hong Kong, Hong Kong. Prof. Lai has been selected as the Academician of the International Academy of Systems and Cybernetic Sciences (Austria) and the Changjiang Scholar Chair Professor by the Ministry of Education (China). He has published over 30 books and more than 400 international refereed journal papers. His main research interests include supply chain and operations management, business analytics, computational intelligence, and financial risk management.

Predrag Rajkovi , Ph.D., D.Sc., is a Professor at the Department of Mathematics and Informatics, of Mechanical Engineering Faculty at the University of Ni, Ni, Serbia. He published over 150 scientific papers and a monograph mainly dealing with the mathematical disciplines: Special functions, Numerical Analysis, Mathematical Programming, and Optimization. He has been on the editorial boards and reviewer of several respected international journals. He has been a visiting professor at the University in Kassel, Germany; Waterford Institute in Ireland; Malardalen University in Sweden and Masaryk University in Czech. In his almost 40 years of teaching experience, he has published 4 textbooks. He was an advisor for two doctoral dissertations and a foreign examiner for more than ten of them. He had participated in 10 international and domestic projects and more than 50 conferences, often as a member of the organizing and scientific committees.

Contenu

Historical Note on Unconstrained Optimization and Quantum Calculus.- Basics of Unconstrained Optimization and Quantum Calculus.- Quantum-Steepest Descent Method with Quasi-Fejér Convergence.- Quantum-

Fletcher-Reeves Conjugate Gradient Method.- Quantum-Polak-Ribière-Polyak.- Conjugate Gradient Method.-Quantum-Dai-Yuan Conjugate Gradient Method.- Quantum-Broyden-Fletcher-Goldfarb-Shanno

Method.- Quantum-Limited Memory Broyden-Fletcher-Goldfarb-Shanno Method.