Potential Function Methods For Approximately Solving Linear Programming Problems breaks new ground in linear programming theory. The book draws on the research developments in three broad areas: linear and integer programming, numerical analysis, and the computational architectures which enable speedy, high-level algorithm design. During the last ten years, a new body of research within the field of optimization research has emerged, which seeks to develop good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context of the modern theory of algorithms. The result of this work, in which Daniel Bienstock has been very much involved, has been a family of algorithms with solid theoretical foundations and with growing experimental success. This book will examine these algorithms, starting with some of the very earliest examples, and through the latest theoretical and computational developments.

This volume contains the papers accepted for publication at IPCO X, the Tenth InternationalConferenceonInteger ProgrammingandCombinatorialOptimi- tion, held in New York City, New York, USA, June 7-11, 2004.The IPCO series of conferences presents recent results in theory, computation and applications of integer programming and combinatorial optimization. These conferences are sponsoredby the Mathematical ProgrammingSociety, andareheldin thoseyearsin whichno InternationalSymposiumonMathema- calProgrammingtakes place.IPCO VIII was held in Utrecht (The Netherlands) and IPCO IX was held in Cambridge (USA). A total of 109 abstracts, mostly of very high quality, were submitted. The ProgramCommittee accepted 32, in order to meet the goal of having three days of talks with no parallel sessions. Thus, many excellent abstracts could not be accepted. The papers in this volume havenot been refereed. It is expected that revised versions of the accepted papers will be submitted to standard scienti?c journals for publication. The Program Committee thanks all authors of submitted manuscripts for their support of IPCO. March 2004 George Nemhauser Daniel Bienstock Organization IPCO X was hosted by the Computational Optimization Research Center (CORC), Columbia University.

Potential Function Methods For Approximately Solving Linear Programming Problems breaks new ground in linear programming theory. The book draws on the research developments in three broad areas: linear and integer programming, numerical analysis, and the computational architectures which enable speedy, high-level algorithm design. During the last ten years, a new body of research within the field of optimization research has emerged, which seeks to develop good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context of the modern theory of algorithms. The result of this work, in which Daniel Bienstock has been very much involved, has been a family of algorithms with solid theoretical foundations and with growing experimental success. This book will examine these algorithms, starting with some of the very earliest examples, and through the latest theoretical and computational developments.

This book constitutes the refereed proceedings of the 21st International Conference on Integer Programming and Combinatorial Optimization, IPCO 2020, held in London, UK, in June 2020. The 33 full versions of extended abstracts presented were carefully reviewed and selected from 126 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, computation, and applications in these areas.

The power grid can be considered one of twentieth-century engineering's greatest achievements, and as grids and populations grow, robustness is a factor that planners must take into account. Power grid robustness is a complex problem for two reasons: the underlying physics is mathematically complex, and modeling is complicated by lack of accurate data. This book sheds light on this complex problem by introducing the engineering details of power grid operations from the basic to the detailed; describing how to use optimization and stochastic modeling, with special focus on the modeling of cascading failures and robustness; providing numerical examples that show "how things work"; and detailing the application of a number of optimization theories to power grids.?????