## Applied Mathematics Colloquium: Dr. Goran Lesaja

#### Georgia Southern University

**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.