The introduction of Karmarkar's polynomial algorithm for linear programming (LP) in 1984 has influenced wide areas in the field of optimization. While in 80s emphasis was on developing and implementing efficient variants of interior point methods for LP, the nineties have shown applicability to certain structured nonlinear programming and combinatorial problems. We will give a historical account of the developments and outline the major contributions to the field in the last decade. An important class of problems to which interior point methods are applicable is semidefinite optimization, which has recently gained much attention. It has a lot of applications in various fields (like control and system theory, combinatorial optimization, algebra, statistics, structural design) and can be efficiently solved with interior point methods.
Report 95-45, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, 1995.