Tamás Rapcsák - Böcker

This is a differential geometric approach to smooth nonlinear optimization. This allows the author to improve the sufficiency part of the Lagrange multiplier rule introduced in 1788 and to solve Fenchel's problem of level sets (1953) in the smooth case. Furthermore, this permits the author to replace convexity by geodesic convexity and apply it in complementarity systems, to study the nonlinear coordinate representations of smooth optimization problems, to describe the structure by tensors, to introduce a general framework for variable metric methods containing many basic nonlinear optimization algorithms and, last but not least, to generate a class of polynomial interior point algorithms for linear optimization by a subclass of Riemannian metrics.

This text is dedicated to the memory of Steven Vajda, one of the pioneers of mathematical programming, who was born in Hungary. The 22 invited chapters written by 36 authors from 12 countries provide the reader with an insight into some advances in mathematical programming. The book is addressed to researchers and postgraduate students with an interest in the theoretical and algorithmic aspects of the field.

This volume contains refereed papers based on lectures presented at the XIV International Conference on Mathematical Programming, held at Matrahaza, Hungary. The main purpose of the conference was to review and discuss advances and promising research trends concerning theory, algorithms, and applications in the fields of optimization theory, and related areas such as convex analysis, complementarity systems, and variational inequalities.

This book is dedicated to the memory of Steven Vajda, one of the pioneers of mathematical programming, who was born in Hungary. The twenty-two invited chapters written by thirty-six authors from twelve countries provide the reader with an insight into recent advances in mathematical programming. Audience: This book is addressed to researchers and postgraduate students with an interest in the theoretical and algorithmic aspects of the field.

Experience gained during a ten-year long involvement in modelling, program­ ming and application in nonlinear optimization helped me to arrive at the conclusion that in the interest of having successful applications and efficient software production, knowing the structure of the problem to be solved is in­ dispensable. This is the reason why I have chosen the field in question as the sphere of my research. Since in applications, mainly from among the nonconvex optimization models, the differentiable ones proved to be the most efficient in modelling, especially in solving them with computers, I started to deal with the structure of smooth optimization problems. The book, which is a result of more than a decade of research, can be equally useful for researchers and stu­ dents showing interest in the domain, since the elementary notions necessary for understanding the book constitute a part of the university curriculum. I in­ tended dealing with the key questions of optimization theory, which endeavour, obviously, cannot bear all the marks of completeness. What I consider the most crucial point is the uniform, differential geometric treatment of various questions, which provides the reader with opportunities for learning the structure in the wide range, within optimization problems. I am grateful to my family for affording me tranquil, productive circumstances. I express my gratitude to F.

This volume contains refereed papers based on the lectures presented at the XIV International Conference on Mathematical Programming held at Matrahaza, Hungary, between 27-31 March 1999. This conference was organized by the Laboratory of Operations Research and Deci­ sion Systems at the Computer and Automation Institute, Hungarian Academy of Sciences. The editors hope this volume will contribute to the theory and applications of mathematical programming. As a tradition of these events, the main purpose of the confer­ ence was to review and discuss recent advances and promising research trends concerning theory, algorithms and applications in different fields of Optimization Theory and related areas such as Convex Analysis, Complementarity Systems and Variational Inequalities. The conference is traditionally held in the Matra Mountains, and housed by the resort house of the Hungarian Academy of Sciences. This was the 14th event of the long lasting series of conferences started in 1973. The organizers wish to express their thanks to the authors for their contributions in this volume, and the anonymous referees for their valu­ able comments. Special thanks are directed to our sponsors, the Hun­ garian Academy of Sciences, the National Committee for Technological Development, the Hungarian National Science Foundation, and last but not least, the Hungarian Operational Research Society. We would like to thank John Martindale from Kluwer Academic Publishers for helping us produce this volume, Eva Nora Nagy for cor­ rections and proof-readings, and Peter Dombi for his excellent work on typesetting and editing the manuscript.