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.

Polynomial optimization have been a hot research topic for the past few years and its applications range from Operations Research, biomedical engineering, investment science, to quantum mechanics, linear algebra, and signal processing, among many others. In this brief the authors discuss some important subclasses of polynomial optimization models arising from various applications, with a focus on approximations algorithms with guaranteed worst case performance analysis. The brief presents a clear view of the basic ideas underlying the design of such algorithms and the benefits are highlighted by illustrative examples showing the possible applications.

This timely treatise will appeal to researchers and graduate students in the fields of optimization, computational mathematics, Operations Research, industrial engineering, and computer science."

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.

This volume contains the papers presented at the International Workshop on Internet and Network Economics held during December 17-20, 2008, in Sha- hai, China, for its fourth edition. WINE 2008 provided a forum for researchers from di?erent disciplines to communicate with each other and exchange their researching ?ndings in this emerging ?eld. WINE 2008hadteninvitedspeakers: FanChungGraham, MatthewJackson, Lawrence Lau, Tom Luo, Eric Maskin, Paul Milgrom, Christos Papadimitriou, Herbert Scarf, Hal Varian and Yinyu Ye. There were 126 submissions. Each submission was reviewed on average by 2. 5 Programme Committee members. The Committee decided to accept 68 papers. The programme also included 10 invited talks. This ?nal program contained papers covering topics including equilibrium, information markets, sponsored auction, network economics, mechanism - sign, socialnetworks, advertisementpricing, computationalequilibrium, network games, algorithms and complexity for games. December 2008 Christos Papadimitriou Shuzhong Zhang Organization Programme Chairs Conference Chair Herbert E. Scarf (Yale University) Program Co-chair Christos Papadimitriou (UC Berkeley) Program Co-chair Shuzhong Zhang (Chinese University of Hong Kong) Local Organizing Committee Chairs Committee Chair Yifan Xu (Fudan University) Committee Co-chair Duan Li (Chinese University of Hong Kong) Committee Co-chair ShouyangWang(ChineseAcademyofSciences) Committee Co-chair Xiaoping Zhao (SSE INFONE