Title : A non-polyhedral primal active set approach for Semidefinite
        and Second Order Cone Programming


			 S. Kartik Krishnan
		   Dept. of Computing & Software,
		        McMaster University,
		       1280 Main Street West,
		  Hamilton, Ontario L8S 4K1, Canada
		    kartik@optlab.cas.mcmaster.ca
		   http://www.caam.rice.edu/~kartik

Abstract :
We present a non-polyhedral primal active set approach for semidefinite
programming (SDP) which mimics the primal simplex method for
linear programming, and exploits the low rank of the extreme
point solutions of the primal feasible region. The goal is to find a proper 
superset of the range space of an optimal extreme point solution. The
algorithm generates a sequence of primal iterates with non-increasing 
objecive values. Under a nondegeneracy assumption, the objective values are 
strictly decreasing. We will discuss the convergence of the algorithm,
and some preliminary computational results. We also 
relate this method to other cutting plane approaches that have been
introduced for the SDP. If time permits, we will also consider
extensions for Second Order Cone Programming (SOCP)