About the Book
This volume includes chapters on topics presented at the conference on Recent Trends in Convex Optimization: Theory, Algorithms and Applications (RTCOTAA-2020), held at the Department of Mathematics, Indian Institute of Technology Patna, Bihar, India, from 29–31 October 2020. It discusses a comprehensive exploration of the realm of optimization, encompassing both the theoretical underpinnings and the multifaceted real-life implementations of the optimization theory. It meticulously features essential optimization concepts, such as convex analysis, generalized convexity, monotonicity, etc., elucidating their theoretical advancements and significance in the optimization sphere. Multiobjective optimization is a pivotal topic which addresses the inherent difficulties faced in conflicting objectives. The book delves into various theoretical concepts and covers some practical algorithmic approaches to solve multiobjective optimization, such as the line search and the enhanced non-monotone quasi-Newton algorithms. It also deliberates on several other significant topics in optimization, such as the perturbation approach for vector optimization, and solution methods for set-valued optimization. Nonsmooth optimization is extensively covered, with in-depth discussions on various well-known tools of nonsmooth analysis, such as convexificators, limiting subdifferentials, tangential subdifferentials, quasi-differentials, etc.
Notable optimization algorithms, such as the interior point algorithm and Lemke’s algorithm, are dissected in detail, offering insights into their applicability and effectiveness. The book explores modern applications of optimization theory, for instance, optimized image encryption, resource allocation, target tracking problems, deep learning, entropy optimization, etc. Ranging from gradient-based optimization algorithms to metaheuristic approaches such as particle swarm optimization, the book navigates through the intersection of optimization theory and deep learning, thereby unravelling new research perspectives in artificial intelligence, machine learning and other fields of modern science. Designed primarily for graduate students and researchers across a variety of disciplines such as mathematics, operations research, electrical and electronics engineering, computer science, robotics, deep learning, image processing and artificial intelligence, this book serves as a comprehensive resource for someone interested in exploring the multifaceted domain of mathematical optimization and its myriad applications.
Table of Contents:
P. Marechal, Elements of Convex Analysis.- T. Antczak, Solution Concepts in Vector Optimization – an Overview.- J.-P. Crouzeix, Generalized Convexity and Generalized Monotonicity.- N. Dinh, D. H. Long, A Perturbation Approach to Vector Optimization Problems.- K. Som, V. Vetrivel, Results on Existence of l-Minimal and u-Minimal Solutions in Set-Valued Optimization: a Brief Survey.- Q. H. Ansari, N. Hussain, Pradeep Kumar Sharma, Scalarization for Set Optimization in Vector Spaces.- A. K. Das, A. Dutta, R. Jana, Complementarity Problems and Its Relation with Optimization Theory.- B. Kohli, Convexificators and Their Role in Nonsmooth Optimization.- S. Treanta, N. Abdulaleem, On Variational Derivative and Controlled Variational Inequalities.- L. T. Tung, Tangential Subdifferential and Its Role in Optimization.- K. Som, J. Dutta, Limiting subdifferential and its role in optimization.- V. Laha, H. N. Singh, S. K. Mishra, On Quasidifferentiable Mathematical Programs with Vanishing Constraints.- N. Kanzi, A. Kabgani, G. Caristi, D. Barilla, On Nonsmooth Semi-Infinite Programming Problems.- P. Marechal, Entropy Optimization.- S. K. Neogy, G. Singh, Lemke’s Algorithm and a Class of Convex Optimization Problem.- S. K. Neogy, R. Chakravorty, S. Ghosh, Interior Point Methods for Some Special Classes of Optimization Problems.- G. Panda, M. A. T. Ansary, Review on Line Search Techniques for Nonlinear Multi-objective Optimization Problems.- K. Kumar, A. Singh, A. Upadhayay, D. Ghosh, An Improved Nonmonotone Quasi-Newton Method for Multiobjective Optimization Problems.- A. K. Agrawal, S. Yadav, A. Chouksey, A. Ray, Particle Swarm Optimization and Its role in Solving Unconstrained and Constrained Optimization Problems.- E. Pauwels, Introduction to Optimization for Deep Learning.- G. Shukla, N. D. Chaturvedi, Optimization in Resource Allocation Network.- M. Kumar, B. Mishra, N. Deep, A Survey on Optimized Based Image Encryption Techniques.- U. Asfia and R. Radhakrishnan, Parametrised Maximum Correntropy Estimation for 2D and 3D Angles-Only Target Tracking Problem.
About the Author :
Balendu Bhooshan Upadhyay is Associate Professor at the Department of Mathematics, Indian Institute of Technology Patna, Bihar, India. Earlier, he worked as a post-doctoral fellow of the National Board of Higher Mathematics (NBHM) at Banaras Hindu University, from May–December 2014. After that, he was Assistant Professor at the National Institute of Technology Manipur. He obtained his PhD from Banaras Hindu University, Varanasi, Uttar Pradesh, India. His research interests include topics on variational inequalities, nonlinear multiobjective optimization, numerical optimization and mathematical programming problems on differentiable manifolds. He has published more than 50 research papers in various national and international journals of repute and coauthored a book, Pseudolinear Function and Optimization, with Shashi Kant Mishra. He has supervised 2 PhD theses, 3 M.Tech. and 9 M.Sc. dissertations. Currently, he is guiding 5 PhD students including 2 PMRF fellows, thus fostering the growth of young researchers in optimization.
He has received numerous honours and accolades in his academic and professional career. In 2023–2024, he was awarded the Science and Engineering Research Board (SERB)-International Research Experience (SIRE) fellowship to conduct research at the Rochester Institute of Technology, Rochester, New York, USA. He was also offered a travel grant by SERB to attend the 9th International Conference on Optimization Techniques and Application in Taiwan, in 2013. He was awarded the IMS Prize in 2012 for presenting the Best Research Paper at the 78th Annual Conference of IMS. He is the Academic Editor of the International Journal of Mathematics in Operations Research. In addition, he has been prolifically involved in various academic and administrative responsibilities. He has organized and chaired sessions of several conferences and workshops at national and international levels.
Shashi Kant Mishra is Professor at the Department of Mathematics, Institute of Science, Banaras Hindu University (BHU), Varanasi, Uttar Pradesh, India, since 2014, where he joined as Associate Professor in 2008. Earlier, he held faculty positions at Raja Balwant Singh College, Agra, and G. B. Pant University of Agriculture and Technology, Pant Nagar. He completed his PhD from the Indian Institute of Technology (Banaras Hindu University), Varanasi, India, in 1995. He was awarded a D.Sc. from Dr Bhimrao Ambedkar University, Agra, Uttar Pradesh, in 2002. His research domains span a range of topics, including multiobjective optimization, linear and nonlinear programming, variational inequalities, nonsmooth analysis, generalized convexity and numerical optimization, etc. He has authored 10 books, including textbooks and monographs, and has been on the Editorial Boards of several respected international journals. With more than 200 research papers published in various national and international journals of repute, he has guest-edited special issues of the Journal of Global Optimization and Optimization Letters (both Springer Nature) and Optimization (Taylor & Francis).
He has supervised 22 PhD students, thus nurturing the development of young researchers in optimization. He has conducted research visits to more than 15 institutes/universities in various countries such as France, Canada, Italy, Spain, Japan, Taiwan, China, Singapore, Vietnam and Kuwait. He received recognition at state and national levels, including the Young Scientist award from the Department of Science and Technology, Government of India (2001–2002) for his pioneering research. He received the Indian National Science Academy (INSA) Teacher Award (2020–2021). He has also been part of esteemed committees at reputed academic institutions, such as a member of the academic council at Jawaharlal Nehru University (May 2016–November 2019) and a member of the selection committee of Aligarh Muslim University, since May 2016. Moreover, he has been extensively engaged in multiple academic and administrative duties. This involvement extends to organizing and presiding sessions at numerous nationally and internationally renowned conferences and workshops.
Pierre Maréchal is a Professor of Mathematics at the University of Toulouse III – Paul Sabatier, France, since February 2005. His career is distinguished by a diverse academic trajectory, beginning as an Assistant Lecturer at the University of Toulouse (1996–1997), followed by a postdoctoral fellowship at Simon Fraser University in Vancouver, Canada (1997–1999), and later as an Associate Professor at the University of Montpellier (1999–2005). Throughout his career, he has embraced international collaboration, spending a year at the École Polytechnique Fédérale de Lausanne, Switzerland, and a six-month research leave at the University of Victoria, Canada.
Pierre Maréchal has devoted his career to advancing optimization theory and its wide-ranging applications, including inverse problems, convex optimization, and signal processing. His research has found applications in areas such as aperture synthesis, medical imaging and statistics. He has published more than 46 research papers and supervised eight PhD theses, playing an active role in mentoring the next generation of researchers. His academic foundation includes an engineering diploma from ENSICA, Toulouse, and a Master’s degree in signal and image processing, where he graduated with honours and as valedictorian. He earned his PhD from the University of Toulouse, focusing on the regularization of ill-posed problems, particularly in the context of signal and image processing for astronomy. In addition to his research and teaching, he has contributed to the academic community through various leadership roles, including serving on the organizing committees of several international conferences and seminars. His excellence in research has been recognized with the prestigious Prime d’Excellence Scientifique award in 2010.
