There has been much recent progress in approximation algorithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. In discrete (or combinatorial) optimization many approaches have been developed recently that link the discrete universe to the continuous universe through geomet- ric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. As a result new ap- proximate algorithms have been discovered and many new computational approaches have been developed....

2 Radiant sets 236 3 Co-radiant sets 239 4 Radiative and co-radiative sets 241 5 Radiant sets with Lipschitz continuous Minkowski gauges 245 6 Star-shaped sets and their kernels 249 7 Separation 251 8 Abstract convex star-shaped sets 255 References 260 11 DIFFERENCES OF CONVEX COMPACTA AND METRIC SPACES OF CON- 263 VEX COMPACTA WITH APPLICATIONS: A SURVEY A. M. Rubinov, A. A. Vladimirov 1 Introduction 264 2 Preliminaries 264 3 Differences of convex compact sets: general approach 266 4 Metric projections and corresponding differences (one-dimensional case) 267 5 The *-difference 269 6 The...

Special tools are required for examining and solving optimization problems. The main tools in the study of local optimization are classical calculus and its modern generalizions which form nonsmooth analysis. The gradient and various kinds of generalized derivatives allow us to ac- complish a local approximation of a given function in a neighbourhood of a given point. This kind of approximation is very useful in the study of local extrema. However, local approximation alone cannot help to solve many problems of global optimization, so there is a clear need to develop special global tools for...

Everything should be made as simple as possible, but not simpler. (Albert Einstein, Readers Digest, 1977) The modern practice of creating technical systems and technological processes of high effi.ciency besides the employment of new principles, new materials, new physical effects and other new solutions ( which is very traditional and plays the key role in the selection of the general structure of the object to be designed) also includes the choice of the best combination for the set of parameters (geometrical sizes, electrical and strength characteristics, etc.) concretizing this general...

People are facing more and more NP-complete or NP-hard problems of a combinatorial nature and of a continuous nature in economic, military and management practice. There are two ways in which one can enhance the efficiency of searching for the solutions of these problems. The first is to improve the speed and memory capacity of hardware. We all have witnessed the computer industry's amazing achievements with hardware and software developments over the last twenty years. On one hand many computers, bought only a few years ago, are being sent to elementary schools for children to learn the...

In this edition, the scope and character of the monograph did not change with respect to the first edition. Taking into account the rapid development of the field, we have, however, considerably enlarged its contents. Chapter 4 includes two additional sections 4.4 and 4.6 on theory and algorithms of D.C. Programming. Chapter 7, on Decomposition Algorithms in Nonconvex Optimization, is completely new. Besides this, we added several exercises and corrected errors and misprints in the first edition. We are grateful for valuable suggestions and comments that we received from several colleagues....

Nonsmoothness and nonconvexity arise in numerous applications of mechan ics and modeling due to the need for studying more and more complicated phe nomena and real life applications. Mathematicians have started to provide the necessary tools and theoretical results underpinning these applications. Ap plied mathematicians and engineers have begun to realize the benefits of this new area and are adopting, increasingly, these new tools in their work. New computational tools facilitate numerical applications and enable the theory to be tested, and the resulting feedback poses new theoretical...

l. i ALSTED, MEDE ANDTHE BIRTH OFCALVINIST MILLENARIANISM In the past thirty to forty years, the spread and influence of millenarianism within the Protestant world has been traced from the Reformation to the present day by dozens of scholarly studies. ' Medieval historians have lo- ted echoes in the modem world ofeschatological innovations deriving from 2 their period, above all those originating with Joachim of Fiore. Social and political historians, attracted especially by the function of millenarianism as a proto-revolutionary ideology, have focused on its influences at times of acute...

Contributions by leading experts and others to understanding the crucial role of metacognition in relation to broad areas of education make this collection a uniquely stimulating book. It encompasses metacognition in both the neglected area of teaching and the more well-established area of learning. The twelve chapters contribute to our understanding of the construct of metacognition and to its role in both teaching and learning. It addresses domain-general and domain-specific aspects of metacognition, including applications to the particular subjects of reading, speaking, mathematics, and...

On August 1997 a conference titled "From Local to Global Optimiza tion" was held at Storgarden in Rimfor.sa near the Linkoping Institute of Technology, Sweden. The conference gave us the opportunity to cel ebrate Hoang Thy's achievements in Optimization during his 70 years of life. This book consists of a collection of research papers based on results presented during the conference and are dedicated to Professor Hoang Thy on the occasion of his 70th birthday. The papers cover a wide range of recent results in Mathematical Pro gramming. The work of Hoang Thy, in particular in Global Optimiza...