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.

本書提供了對連續優化和變分不等式理論和方法的全面涵蓋。它描述了平滑和非平滑函數優化的理論和解決方法，單值和多值映射的變分不等式，以及混合變分不等式、互補問題和一般均衡問題等相關類別的理論和解決方法。重點在於揭示這些問題的通用特性，以便創建高效的解決方法。

主要特點包括：
- 本書深入廣泛地介紹了由優化技術和變分不等式控制的過程的理論。
- 提供了多種解決方法，幫助讀者開發可以通過涉及線性和非線性函數的優化技術建模的現實問題的各種優化工具。
- 本書關注非線性現象的最新研究成果，這些現象可能出現在人類活動的各個領域。
- 本書還以清晰簡單的方式介紹相關數學，以幫助解決機械工程、管理、控制行為、交通信號、工業等各個領域的實際問題。

本書主要面向攻讀計算機工程和電氣工程課程的高年級本科生和研究生。研究人員、學者和業界人士也會發現本書有用。

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 Lo´dz´, Lo´dz´, Poland. He has obtained his Master in mathematics at Faculty of Mathematics, Physics and Chemistry, University of Lo´dz´, Lo´dz´, Poland. He has received his PhD degree in mathematics at Faculty of Mathematics and Computer Science, University of Lo´dz´, Lo´dz´, Poland. He has obtained a postdoctoral degree in mathematics also at Faculty of Mathematics and Computer Science, University of Lo´dz´, Lo´dz´, Poland. He has more than 30 years of academic experience and teaching in Faculty of Mathemat- ics and Computer Science, University of Lo´dz´, Lo´dz´, 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.

Anurag Jayswal是印度達恩巴德印度理工學院數學與計算系的副教授。他在印度瓦拉納西的巴納拉斯印度大學獲得數學碩士學位，並獲得一等榮譽。他在巴納拉斯印度大學數學系獲得數學博士學位。他曾獲得印度科技部的青年科學家計劃。他擁有超過15年的學術經驗，在BIT Mesra、Ranchi和印度理工學院教授。他的研究興趣包括連續優化、非光滑優化、廣義凸性、控制理論和變分不等式問題。他是連續優化和變分不等式領域100多篇期刊論文的作者和合著者，並指導了10多名博士生。他是印度Opsearch和美國Advances in Variational Inequalities的編輯委員會成員。他曾訪問多個國家，在國際會議上發表演講。他是多個國際期刊的審稿人。

Tadeusz Antczak是波蘭羅茲大學數學與計算機科學學院的副教授。他在波蘭羅茲大學數學、物理和化學學院獲得數學碩士學位，並在波蘭羅茲大學數學與計算機科學學院獲得數學博士學位。他還在波蘭羅茲大學數學與計算機科學學院獲得了博士後學位。他擁有超過30年的學術經驗，在波蘭羅茲大學數學與計算機科學學院教授。他的研究興趣包括連續優化、多目標規劃、非光滑優化、廣義凸性、控制理論、變分不等式問題和關聯數據庫。他是連續優化領域100多篇期刊論文的作者和合著者，並是美國Advances in Nonlinear Variational Inequalities（ANVI）和羅馬尼亞Journal of Advanced Mathematical Studies的編輯委員會成員。他參加過多個國際會議，並是多個國際期刊的審稿人。