High Performance Optimization

For a long time the techniques of solving linear optimization (LP) problems improved only marginally. In the mid 1970s 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 developments in "High Performance Optimization Techniques". The first part is a treatment of interior point methods for semidefinite programming problems. The second part reviews research topics and results in the area of convex optimization.