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Exact penalty function algorithm with simple updating of the penalty parameter

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Abstract

A new globally convergent algorithm for minimizing an objective function subject to equality and inequality constraints is presented. The algorithm determines a search direction by solving a quadratic programming subproblem, which always has an optimal solution, and uses an exact penalty function to compute the steplength along this direction through an Armijo-type scheme. The special structure of the quadratic subproblem is exploited to construct a new and simple method for updating the penalty parameter. This method may increase or reduce the value of the penalty parameter depending on some easily performed tests. A new method for updating the Hessian of the Lagrangian is presented, and a Q-superlinear rate of convergence is established.

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Authors and Affiliations

  1. Department of Mathematics, Federal University of Maranhão, São Luis, Maranhão, Brazil

    J. F. A. De O. Pantoja (Adjunct Professor)

  2. Electrical Engineering Department, Imperial College, University of London, London, England

    D. Q. Mayne (Professor)

Authors
  1. J. F. A. De O. Pantoja
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  2. D. Q. Mayne
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Additional information

This work was supported in part by the British Council and the Conselho Nacional de Desenvolvimento Cientifico & Tecnologico/CNPq, Rio de Janeiro, Brazil.

The authors are very grateful to Mr. Lam Yeung for his invaluable assistance in computing the results and to a reviewer for constructive advice.

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Pantoja, J.F.A.D.O., Mayne, D.Q. Exact penalty function algorithm with simple updating of the penalty parameter. J Optim Theory Appl 69, 441–467 (1991). https://doi.org/10.1007/BF00940684

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