Interior-Point and Active-Set Algorithms for Nonlinear Optimization

Event Sponsor: 
Mathematics and Computer Science Division Seminar
Start Date: 
Feb 19 2008 (All day)
Building/Room: 
Building 221 Conference Room A216
Location: 
Argonne National Laboratory
Speaker(s): 
Lifeng Chen
Speaker(s) Title: 
Columbia University
Host: 
Sven Leyffer

We will present an interior-point L-2 penalty method for nonlinear programming, and show that it enjoys strong global and local convergence properties. We will discuss a particular implementation of the method that incorporates a recently proposed piecewise linear penalty method (PLPM). The PLPM is a penalty variant of the filter method. It gives a mechanism for automatically choosing penalty parameters. We will show that the numerical performance of the method is competitive with state-of-the-art interior codes. If there is still time, I will briefly discuss an active-set method for mathematical programs with linear complementarity constraints (MPLCC). We will show that simple pivot strategies similar to those used in simplex method for LP can be adopted here to handling MPLCC. These strategies are cheaper to implement than existing approaches. They also guarantee convergence of the iterates to first-order stationary points, instead of other weak stationary points that may be accumulation points for existing algorithms.

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