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QPAL -- A solver of convex quadratic optimization problems, using an augmented Lagrangian approach

Jean Charles Gilbert 1

(2009)

QPAL is a piece of software that aims at solving a convex quadratic optimization problem with linear equality and inequality constraints. The implemented algorithm uses an augmented Lagrangian approach, which relaxes the equality constraints and deals explicitely with the bound constraints on the original and slack variables. The generated quadratic functions are minimized on the activated faces by a truncated conjugate gradient algorithm, interspersed with gradient projection steps. When the optimal value is finite, convergence occurs at a linear speed that can be prescribed by the user. Matrices can be strored in dense or sparse structures; in addition, the Hessian of the quadratic objective function may have a direct of inverse $\ell$-BFGS form. QPAL is written in Fortran-2003.

1:	ESTIME (INRIA Paris-Rocquencourt)
	INRIA

Domain

:

Mathematics/Optimization and Control Computer Science/Operations Research

Keywords: augmented lagrangian – convex quadratic optimization – dense and sparse matrices – gradient projection – l-BFGS matrix – linear convergence

inria-00442295, version 1

http://hal.inria.fr/inria-00442295

oai:hal.inria.fr:inria-00442295

From: Jean Charles Gilbert <>

Submitted on: Saturday, 19 December 2009 15:08:48

Updated on: Wednesday, 20 January 2010 10:41:19