Interior point optimization methods: Theory, implementations and engineering applications

The objective of this paper is to present, in a tutorial way, the basic ideas involved in Narendra Karmarkar's projective scaling algorithm for solving linear programming problems and to show two of its most important extensions, the dual and the dual affine algorithms. Implementation issues regarding the practical solution of the search direction are also discussed. A new parallel preconditioned conjugate gradient solution technique is introduced. This parallel search direction solver provides almost perfect p speedup for p processors. A summary of application results on a very large scale integration (VLSI) circuit layout and economic dispatch in power systems is presented. In all these applications, the interior point methods exhibit an average speedup of about six to 100 times over a well-known MINOS simplex code.