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Since the early 1960s, polyhedral methods have played a central role in both the theory and practice of combinatorial optimization. Since the early 1990s, a new technique, semidefinite programming, has been increasingly applied to some combinatorial optimization problems. The semidefinite programming problem is the problem of optimizing a linear function of matrix variables, subject to finitely many linear inequalities and the positive semidefiniteness condition on some of the matrix variables. On certain problems, such as maximum cut, maximum satisfiability, maximum stable set and geometric representations of graphs, semidefinite programming techniques yield important new results. This mono...
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
This book is the largest referral for Turkish companies.
This book is the largest referral for Turkish companies.
This invaluable book contains 19 papers selected from those submitted to a conference held in Hong Kong in July 2000 to celebrate the 70th birthday of Professor Steve Smale. It may be regarded as a continuation of the proceedings of SMALEFEST 1990 ("From Topology to Computation") held in Berkeley, USA, 10 years before, but with the focus on the area in which Smale worked more intensively during the '90's, namely the foundations of computational mathematics.
This new edition of the well established text Scheduling - Theory, Algorithms, and Systems provides an up-to-date coverage of important theoretical models in the scheduling literature as well as significant scheduling problems that occur in the real world. It again includes supplementary material in the form of slide-shows from industry and movies that show implementations of scheduling systems. The main structure of the book as per previous edition consists of three parts. The first part focuses on deterministic scheduling and the related combinatorial problems. The second part covers probabilistic scheduling models; in this part it is assumed that processing times and other problem data ar...
Semidefinite programming (SDP) is one of the most exciting and active research areas in optimization. It has and continues to attract researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This tremendous research activity has been prompted by the discovery of important applications in combinatorial optimization and control theory, the development of efficient interior-point algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory. The Handbook of Semidefinite Programming offers an advanced and broad overview of the current state of the field. It contains nineteen chapters written by the leading experts on the subject. The chapters are organized in three parts: Theory, Algorithms, and Applications and Extensions.
This book constitutes the proceedings of the 15th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2011, held in New York, USA in June 2011. The 33 papers presented were carefully reviewed and selected from 110 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization with the aim to present recent developments in theory, computation, and applications. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.
Symposium held in Miami, Florida, January 22–24, 2006.This symposium is jointly sponsored by the ACM Special Interest Group on Algorithms and Computation Theory and the SIAM Activity Group on Discrete Mathematics.Contents Preface; Acknowledgments; Session 1A: Confronting Hardness Using a Hybrid Approach, Virginia Vassilevska, Ryan Williams, and Shan Leung Maverick Woo; A New Approach to Proving Upper Bounds for MAX-2-SAT, Arist Kojevnikov and Alexander S. Kulikov, Measure and Conquer: A Simple O(20.288n) Independent Set Algorithm, Fedor V. Fomin, Fabrizio Grandoni, and Dieter Kratsch; A Polynomial Algorithm to Find an Independent Set of Maximum Weight in a Fork-Free Graph, Vadim V. Lozin a...
For a long time the techniques of solving linear optimization (LP) problems improved only marginally. Fifteen years ago, however, a revolutionary discovery changed everything. A new `golden age' for optimization started, which is continuing up to the current time. What is the cause of the excitement? Techniques of linear programming formed previously an isolated body of knowledge. Then suddenly a tunnel was built linking it with a rich and promising land, part of which was already cultivated, part of which was completely unexplored. These revolutionary new techniques are now applied to solve conic linear problems. This makes it possible to model and solve large classes of essentially nonlinear optimization problems as efficiently as LP problems. This volume gives an overview of the latest developments of such `High Performance Optimization Techniques'. The first part is a thorough treatment of interior point methods for semidefinite programming problems. The second part reviews today's most exciting research topics and results in the area of convex optimization. Audience: This volume is for graduate students and researchers who are interested in modern optimization techniques.