Optimization, Variational Analysis and Applications

This book includes selected papers presented at the Indo-French Seminar on Optimization, Variational Analysis and Applications (IFSOVAA-2020), held at the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India, from 2-4 February 2020. The book discusses current optimization problems and their solutions by using the powerful tool of variational analysis. Topics covered in this volume include set optimization, multiobjective optimization, mathematical programs with complementary, equilibrium, vanishing and switching constraints, copositive optimization, interval-valued optimization, sequential quadratic programming, bound-constrained optimization, variational inequalities, and more. Several applications in different branches of applied mathematics, engineering, economics, finance, and medical sciences have been included. Each chapter not only provides a detailed survey of the topic but also builds systematic theories and suitable algorithms to deduce the most recent findings in literature. This volume appeals to graduate students as well as researchers and practitioners in pure and applied mathematics and related fields that make use of variational analysis in solving optimization problems.

Auteur

VIVEK LAHA is Assistant Professor at the Department of Mathematics, Institute of Science, Banaras Hindu University (BHU), Varanasi, India, since June 2016. He completed his Ph.D. and M.Sc. from BHU in 2014 and 2009, respectively. His research interests lie in the fields of multiobjective optimization, vector variational inequalities, generalized convexity, nonsmooth analysis, mathematical programs with vanishing constraints, semi-infinite optimization, robust optimization, etc. He has published research articles in several international journals of repute and co-authored two book chapters published by Springer Nature. He has presented his research work in international events at various universities, including Future University Hakodate, Hakodate, Japan; National Taiwan University of Science and Technology (Taiwan Tech), Taipei, Taiwan; Vietnam Institute for Advanced Study in Mathematics (VIASM), Hanoi, Vietnam; Banaras Hindu University, India; University of Delhi, India; Indian Statistical Institute, Delhi; and Indian Statistical Institute, Chennai. He has received the NBHM Postdoctoral Fellowship, CSIR-UGC Senior and Junior Research Fellowships, CSIR Foreign Travel Grant, DST-Purse Foreign Travel Grant, SERB Travel Grant and many more. He is the principal investigator of a project sponsored by the UGC Start-up Grant and is also one of the members of the Working Group on Generalized Convexity and International Society on Multiple Criteria Decision Making.

PIERRE MARECHAL is Professor of Mathematics at Université Paul Sabatier, Toulouse, France. He received his Ph.D. in 1997, master's degree in 1993, and engineering diploma in 1991 form the University of Toulouse, France. Since 1997, he has worked in different positions at the University of Toulouse, France; Simon Fraser University, Vancouver, Canada; and the University of Montpellier, France. His research interests include inverse problems, optimization, convex analysis, calculus of variations, conditional number optimization, and condition number optimization. He has supervised eight Ph.D. students till date and worked in the committee of many scholars. He has delivered invited talks at many international conferences and universities from time to time and organized a number of international conferences and workshops. He has published considerable research articles in international journals of repute.

S. K. MISHRA is Professor at the Department of Mathematics, Institute of Science, Banaras Hindu University (BHU), India. He completed his Ph.D. in Mathematics from BHU in 1995. With a teaching experience of over 22 years, he has guided 18 Ph.D. students so far. He has published several research articles in journals of repute and authored a number of books with renowned publishers. He is the associate editor, managing editor or guest editor of international journals of repute and has organized several national and international conferences/seminars in India and abroad.

Professor Mishra is a member of several professional bodies, including the International Society on Multiple Criteria Decision Making; the Working Group of Generalized Convexity; Pacific Optimization Research Activity Group; and Indian Mathematical Society. He has visited several universities for his academic and research activities, including the Fields Institute for Research in Mathematical Science, Toronto, Canada; Paul Sabatier University, Toulouse, France; Chang Gung University, Taipei, Taiwan; the University of Lorraine, Metz, France; the Muroran Institute of Technology, Japan; Yuan Ze University, Tapipei, Taiwan; the City University of Hong Kong, Hong Kong; University Paul Verlaine, Metz, France; International University, Ho Chi Minh City, Vietnam; University Paul Verlaine, Metz, France; the Institute of Mathematics, Chinese University of Hong Kong, Hong Kong; the Muroran Institute of Technology, Hokkaido, Japan; Kuwait University, Kuwait; the Chinese Academy of Sciences, Beijing; and the National University of Singapore.

Contenu
Khushboo and C. S. Lalitha, Linear and PascolettiSerafini Scalarizations in Unified Set Optimization.- N. K. Bisui, S. Mazumder and G. Panda, A Gradient Free Method for Multiobjective Optimization Problem.- J.-P. Dussault, T. Migot, M. Haddou, The New Butterfly Relaxation Method for Mathematical Programs with Complementarity Constraints.- S. K. Neogy and V. N. Mer, Copositive Optimization and its Applications in Graph Theory.- N Sharma, J. Bisht, and S. K. Mishra, Hermite-Hadamard type Inequalities for Functions whose Derivatives are Strongly-Convex via Fractional Integrals.- Q. H. Ansari, P. K. Sharma, Set Order Relations, Set Optimization and Ekeland's Variational Principle.- A. K. Debnath and D. Ghosh, Characterizations and Generating Efficient Solutions to Interval Optimization Problems.- R. Sadhu, C. Nahak, S. P. Dash, Unconstrained Reformulation of Sequential Quadratic Programming and its Application in Convex Optimization.- P. Maréchal, A Note on Quadratic Penalties for Linear Ill-posed Problems: from Tikhonov Regularization to Mollification.- W. C. Simo Tao Lee.- A New Regularization Method for Linear Exponentially Ill-posed Problems.- V. Laha, H. N. Singh and S. K. Mishra, R. Kumar, On Minimax Programming with Vanishing Constraints.- B. B. Upadhyay and P. Mishra, On Minty Variational Principle for Nonsmooth Interval-Valued Multiobjective Programming Problems.- Y. Pandey, V. Singh, On Constraint Qualifications for Multiobjective Optimization Problems with Switching Constraints.- V. Kapoor and D. Nandan, Optimization of Physico-Chemical Parameters for the Production of Endoxylanase using Combined Response Surface Method and Genetic Algorithm.- A. Kaul, A. Gupta, S. Aggarwal, P. C. Jha, R. Ramanathan, Optimal Duration of Integrated Segment Specific and Mass Promotion Activities for Durable Technology Products: A Differential Evolution Approach.- M. Kumar, A Secure RGB Image Encryption Algorithm in Optimized Virtual Planet Domain.- J. D. Darbari, S. Sharma, M. C. Barrueta Pinto, Identification and Analysis of Key Sustainable Criteria for Third Party Reverse Logistics Provider Selection using the Best-Worst Method.- A. Gupta, N. Pachar, M. C. Barrueta Pinto, Efficiency Assessment through Peer Evaluation and Benchmarking: A Case Study of a Retail Chain using DEA.- R. K. Misra, D. Singh and A. Kumar, Spherical Search Algorithm: A Metaheuristic for Bound-Constrained Optimization.