Abstract
This paper presents an analysis of the involvement of the penalty
parameter in exact penalty function methods that yields modifications
to the standard outer loop which decreases the penalty parameter
(typically dividing it by a constant). The procedure presented is
based on the simple idea of making explicit the dependence of the
penalty function upon the penalty parameter and is illustrated on a
linear programming problem with the $l_1$ exact penalty function and
an active-set approach. The procedure decreases the penalty
parameter, when needed, to the {\em maximal\/} value allowing the
inner minimization algorithm to leave the current iterate. It
moreover avoids unnecessary calculations in the iteration following
the step in which the penalty parameter is decreased. We report on
preliminary computational results which show that this method can require
fewer iterations than the standard way to update the penalty parameter.
This approach permits a better understanding of the performance of exact
penalty methods.
Original language | English |
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Pages (from-to) | 686-699 |
Number of pages | 14 |
Journal | European Journal of Operational Research |
Volume | 83 |
Publication status | Published - 1995 |