Title: Convergence analysis of primal-dual interior and exterior point methods for constrained optimization


			    Igor Griva
			   ORFE, E-Quad, 
		       Princeton University, 
		        Princeton, NJ 08544
		    Email: igriva@princeton.edu

        Authors:  I. Griva, R. Polyak, D. Shanno, R. Vanderbei


Abstract:
We consider two primal-dual algorithms for constrained optimization: interior 
and exterior point methods. The latter is also known as the primal-dual 
nonlinear rescaling method. At each iteration the algorithms solve 
corresponding primal-dual linear systems for finding Newton directions. We 
discuss the linear systems' properties and emphasize their role in global and 
asymptotic convergence analysis of both methods. We formulate convergence 
results for both algorithms. In particular, we establish 1.5-Q-superlinear 
asymptotic rate of convergence of the exterior point method.