Mathematics Colloquium

Mathematics without borders

Department of Mathematics
University of Nebraska at Omaha

WHEN:
On Thursday, September 30, 1999 at 2:20 PM

WHERE:
Durham Science Center, Room 255

WHAT:

Todd Munson

of University of Wisconsin at Madison will give a talk on

Complementarity: Applications and Algorithms.

ABSTRACT:
The standard linear complementarity problem is to find an $x \in \Re^n$ such that the following conditions are satisfied:

$$\begin{array}{c} 0 \le Mx + q, x \ge 0 \\ x^T(Mx + q) = 0, \end{array}$$

where $M \in \Re^{n \times n}$ and $q \in \Re^n$. Applications of this framework are prevalent in various disciplines including economics and engineering. I will motivate the problem using the complementary slackness conditions from linear programming and then develop several extensions and applications.

Many approaches for solving these problems reformulate them as systems of nonsmooth equations and then apply a nonsmooth Newton method. I will discuss one such algorithm, PATH, which is based on the normal map reformulation. Recent theoretical developments concerning PATH are given and practical details about an implementation are presented. I conclude by supplying comparative results of the algorithm on standard test sets against other codes.

Refreshments served 20 minutes prior to the talk in DSC 255

 

 

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  Last modified:   Mon Mar 12 16:39:53 CST 2001