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Publication 00-CNA-06

An interior-point method for a class of saddle point problems

Bjarni V. Halldorsson
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
bjarni@cmu.edu

and

Reha H. Tutuncu
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213, USA
reha+@andrew.cmu.edu

ABSTRACT We present a polynomial time interior-point algorithm for a class of nonlinear saddle-point problems that involve semidefiniteness constraints on matrix variables. These problems originate from robust optimization formulations of convex quadratic programming problems with uncertain input parameters. As an application of our approach we discuss a robust formulation of Markowitz' portfolio selection model.

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