Applied Mathematics Colloquium: Dr. Goran Lesaja

Title: Adaptive Full Newton-step Infeasible Interior-Point Method for Sufficient  Horizontal Linear Complementarity Problems

Speaker: Goran Lesaja, Georgia Southern University

Abstract: An adaptive full Newton-step Infeasible Interior-Point Method  for sufficient Horizontal Linear Complementarity Problem is presented. The adaptive step is obtained by making a convex combination of the affine and centering directions which are obtained by solving the same Newton-type linear system with two different right hand sides, thus  requiring only one factorization per iteration. It is shown that the parameter that defines adaptive step can be chosen  to guarantee the global convergence with iteration bounds that match best known iteration bounds for these types of methods. 

The original method is dependent on the handicap of the problem. However, using the procedure of adaptively updating the handicap until the right one is found, developed by Potra and Liu in 2005, the method can be  modified to solve any sufficient problem with the same order of iteration complexity.