Paper ID sheet
- TITLE: Newton-KKT
for Indefinite Quadratic Programming
- AUTHORS: P.-A. Absil, A. L. Tits.
Two interior-point algorithms are proposed and analyzed, for the (local)
solution of (possibly) indefinite quadratic programming problems. They are of
the Newton-KKT variety in that (much like in the case of primal-dual algorithms
for linear programming) search directions for the `primal´ variables and the
Karush-Kuhn-Tucker (KKT) multiplier estimates are components of the Newton (or
quasi-Newton) direction for the solution of the equalities in the first-order
KKT conditions of optimality or a perturbed version of these conditions. Our
algorithms are adapted from previously proposed algorithms for convex quadratic
programming and general nonlinear programming. First, inspired by recent work
by P. Tseng based on a `primal´ affine-scaling algorithm (à la Dikin)
[J. of Global Optimization, 30 (2004), no 2, 285--300], we consider a simple
Newton-KKT affine-scaling algorithm. Then, a `barrier´ version
of the same algorithm is considered, which reduces to the affine-scaling
version when the barrier parameter is set to zero at every iteration, rather
than to the prescribed value. Global and local quadratic convergence are
proved under nondegeneracy assumptions for both algorithms. Numerical
results on randomly generated problems suggest that the proposed algorithms
may be of great practical interest.
- Key words: interior-point algorithms, primal-dual algorithms, indefinite
quadratic programming, Newton-KKT.
- STATUS: Computational Optimization and Applications, Volume 36, Number 1, January, 2007.