Continuous Optimization and Variational Inequalities

The proposed book provides a comprehensive coverage of theory and methods in the areas of continuous optimization and variational inequality. It describes theory and solution methods for optimization with smooth and non-smooth functions, for variational inequalities with single-valued and multivalued mappings, and for related classes such as mixed variational inequalities, complementarity problems, and general equilibrium problems. The emphasis is made on revealing generic properties of these problems that allow creation of efficient solution methods. Salient Features - The book presents a deep, wide-ranging introduction to the theory of the optimal control of processes governed by optimization techniques and variational inequality - Several solution methods are provided which will help the reader to develop various optimization tools for real-life problems which can be modeled by optimization techniques involving linear and nonlinear functions. - The book focuses on most recent contributions in the nonlinear phenomena, which can appear in various areas of human activities. - This book also presents relevant mathematics clearly and simply to help solve real life problems in diverse fields such as mechanical engineering, management, control behavior, traffic signal, industry, etc. This book is aimed primarily at advanced undergraduates and graduate students pursuing computer engineering and electrical engineering courses. Researchers, academicians and industry people will also find this book useful.

Anurag Jayswal is Associate Professor in the Department of Mathematics and Computing, In- dian Institute of Technology, Dhanbad, India. He obtained his Master in mathematics from Banaras Hindu University, Varanasi, India and was awarded first order of merit. He received his PhD degree in mathematics from the Depart- ment of Mathematics, Banaras Hindu Univer- sity, Varanasi, India. He received a young scien- tist project from the Department of Science and Technology, Government of India. He has more than 15 years of academic experience and teach- ing in BIT Mesra, Ranchi and Indian Institute of Technology, Dhanbad, India. His research interest is continuous optimization, nonsmooth optimization, generalized convexity, control theory and variational inequalities problems. He is the author and coauthor of more than 100 journal papers in the field of continuous optimization and variational inequalities and has supervised more than 10 PhD students. He is editorial board member of Opsearch, India and Advances in Variational Inequalities, USA. He visited several countries to deliver their talks in international conferences. He is a reviewer of various international journals. Tadeusz Antczak is Associate Professor in the Faculty of Mathematics and Computer Science, University of Lödz-, Lödz-, Poland. He has obtained his Master in mathematics at Faculty of Mathematics, Physics and Chemistry, University of Lödz-, Lödz-, Poland. He has received his PhD degree in mathematics at Faculty of Mathematics and Computer Science, University of Lödz-, Lödz-, Poland. He has obtained a postdoctoral degree in mathematics also at Faculty of Mathematics and Computer Science, University of Lödz-, Lödz-, Poland. He has more than 30 years of academic experience and teaching in Faculty of Mathemat- ics and Computer Science, University of Lödz-, Lödz-, Poland. His research interest is continuous optimization, multiobjective programming, nonsmooth optimization, generalized convexity, control theory, variational inequalities problems and relational databases. He is the author and co-author of more than 100 journal papers in the field of continuous optimization. He is an editorial board member of Advances in Nonlinear Vari- ational Inequalities (ANVI), USA, and Journal of Advanced Mathematical Studies, Romania. He participated in several international conferences. He is a reviewer of many international journals.

1. Mixed Type Duality and Saddle Point Criteria for Multiobjective Programming Problems with Nonsmooth Generalized Invexity. 2. Optimality and Duality for Nonsmooth Optimization Problems with Switching Constraints. 3. Optimality Conditions for Approximate Solutions of Nonsmooth Semi-infinite Vector Optimization Problems. 4. Density Aspects in Semi-Infinite Vector Optimization. 5. Optimality Conditions and Duality for Nondifferentiable Multiobjective Fractional Programming Problems. 6. Nonconvex Nonsmooth Minimax Fractional Programming involving Generalized Semidifferentiable Preinvex Functions with Different Directions. 7. Optimality Conditions and Wolfe Duality Results for LU-Efficiency in Differentiable Vector Optimization Problems with Multiple Interval-Valued Objective Function and Vanishing Constraints. 8. Interval-Valued Multi-Time Control Problem with Applications. 9. Generalized Minty and Stampacchia Vector Variational-Like Inequalities and Interval-Valued Vector Optimization Problems. 10. Sufficient Optimality Conditions and Duality for a Nonsmooth Interval-Valued Optimization Problem with Generalized Convexity via gH-Clarke Subgradients. 11. Forward-Backward Extragradient Methods for Quasimonotone Variational Inequalities. 12. Multidimensional Split Variational Inequality in Traffic Analysis. 13. Controlled Nonlinear Dynamics for Constrained Optimization Problems Involving Second-Order Partial Derivatives. 14. A Non-Parametric Dual Control Algorithms of Multidimensional Static Systems with Delay. 15. Well-Posedness of Set Optimization Using Nonlinear Scalarization Function.