Vector optimization is continuously needed in several science fields, particularly in economy, business, engineering, physics and mathematics. The evolution of these fields depends, in part, on the improvements in vector optimization in mathematical programming. The aim of this Ebook is to present the latest developments in vector optimization. The contributions have been written by some of the most eminent researchers in this field of mathematical programming. The Ebook is considered essential for researchers and students in this field.

We always come cross several decision-making problems in our daily life. Such problems are always conflicting in which many different view points should be satisfied. In politics, business, industrial systems, management science, networks, etc. one often encounters such kind of problems. The most important and difficult part in such problems is the conflict between various objectives and goals. In these problems, one has to find the minimum(or maximum) for several objective functions. Such problems are called vector optimization problems (VOP),multi-criteria optimization problems or multi-objective optimization problems. This volume deals with several different topics / aspects of vector optimization theory ranging from the very beginning to the most recent one. It contains fourteen chapters written by different experts in the field of vector optimization.

The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems.The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature.Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems.· Self-contained· Clear style and results are either proved or stated precisely with adequate references· The authors have several years experience in this field· Several subjects (some of them non usual in books of this kind) in one single book, including nonsmooth optimization and vector optimization problems· Useful long references list at the end of each chapter

This is the first full-scale reference grammar of Classical Greek in English in a century. The first work of its kind to reflect significant advances in linguistics made in recent decades, it provides students, teachers and academics with a comprehensive yet user-friendly treatment. The chapters on phonology and morphology make full use of insights from comparative and historical linguistics to elucidate complex systems of roots, stems and endings. The syntax offers linguistically up-to-date descriptions of such topics as case usage, tense and aspect, voice, subordinate clauses, infinitives and participles. An innovative section on textual coherence treats particles and word order and discusses several sample passages in detail, demonstrating new ways of approaching Greek texts. Throughout the book numerous original examples are provided, all with translations and often with clarifying notes. Clearly laid-out tables, helpful cross-references and full indexes make this essential resource accessible to users of all levels.

The techniques described in this monograph form the basis of running an optimally efficient modern day power system. It is a must-read for all students and researchers working on the cutting edge of electric power systems.

The Roman Empire was a society full of gods. So how is it that Christianity come to predominate in this marketplace of competing religions? Why, in just three hundred years, did Christianity go from being an illegal minority faith to being the official religion of the Roman Empire?