#
Warmstarting for Interior Point Methods

Applied to the Long-Term Power Planning Problem

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Technical Report MS 2007-005

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A. Pages,
J. Gondzio and
N. Nabona
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Abstract
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The long-term planning of electricity generation in a liberalised
market using the Bloom and Gallant model can be posed as a
quadratic programming (QP) problem with an exponential number of
linear inequality constraints called load-matching constraints
(LMCs) and several other linear non-LMCs. Direct solution methods
are inefficient at handling such problems and a heuristic
procedure has been devised to generate only those LMCs that are
likely to be active at the optimiser. The problem is then solved
as a finite succession of QP problems with an increasing, though
still limited, number of LMCs, which can be solved efficiently
using a direct method, as would be the case with a QP
interior-point algorithm. Warm starting between successive QP
solutions helps then in reducing the number of iterations
necessary to reach the optimiser.

The warm start technique employed herein is an extension of
Gondzio and Grothey's approach to quadratic programming
problems. We also propose how to initialise new variables
in the problem to which a warm start technique is applied.

This study shows that warm starting requires on average
50\% fewer iterations than a cold start in the test cases solved.
The reduction in computation time is smaller, however.

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Key words:
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Warmstarting, quadratic programming, long-term power generation planning,

interior point method.

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Text
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PDF MS07-005.pdf.

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History:
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Written: August 30, 2007, revised March 13, 2008.

*European Journal on Operational Research* 197 (2009) pp. 112-125.