Message-ID: <Pine.LNX.4.64.0612021303270.8562@gannet.stats.ox.ac.uk>
Date: 2006-12-02T13:09:18Z
From: Brian Ripley
Subject: Quadratic Optimization
In-Reply-To: <17777.21326.6043.444139@stat.math.ethz.ch>
On Sat, 2 Dec 2006, Martin Maechler wrote:
>>>>>> "SpG" == Spencer Graves <spencer.graves at pdf.com>
>>>>>> on Fri, 01 Dec 2006 17:29:56 -0800 writes:
>
> SpG> Unless I'm missing something, optimizing a linear
> SpG> function with quadratic constraints is almost trivial
> SpG> with Langrange multipliers.
>
> yes. Good point, let's hope we're not solving someone's homework
> here :-)
But that is a single equality quadratic constraint, and I believe
'quadratic constraints' (note, plural) conventionally means multiple
inequality constraints. That meaning is a hard problem that needs
specialized software (most likely using interior-point methods).
> SpG> Maximize a'x subject to x'Ax=c.
Not I believe the usual meaning (nor what Googling 'quadratic constraints'
came up with for me).
--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595