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An efficient algorithm for minimizing barrier and penalty functions

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Abstract

Constrained minimization is often done via interior penalty functions. Such functions can be very difficult to minimize using existing algorithms. In this paper, a new algorithm is described which is specially constructed to deal with such functions. It generates search directions by linearizing the objective and constraints about the current (interior) point, substituting these linearizations into the penalty function, and minimizing the result. Properties of the algorithm are derived, an efficient method for solving the direction finding problem is suggested, and computational results are presented. Preliminary results are also given on an extension to quasibarrier and exterior penalty functions.

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Authors and Affiliations

  1. Case Western Reserve University, Cleveland, Ohio, USA

    Leon S. Lasdon

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  1. Leon S. Lasdon
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This document may be reproduced in whole or in part for any non-commercial purpose of the United States Government. Its preparation was supported in part by funds allocated to Case Western Reserve University under contract DAHC 19-68-C-0007 (Project Themis) with the U.S. Army Research Office, Durham Army Materiel Command.

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Lasdon, L.S. An efficient algorithm for minimizing barrier and penalty functions. Mathematical Programming 2, 65–106 (1972). https://doi.org/10.1007/BF01584537

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  • DOI: https://doi.org/10.1007/BF01584537

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