Abstract
This report illustrates, by means of numerical examples, the behavior of the constrained minimization algorithm REQP in situations where the active constraint normals are not linearly independent. The examples are intended to demonstrate that the presence of the penalty parameter in the equations for calculating the Lagrange multiplier estimates enables a useful search direction to be computed. This is shown to be true, whether the dependence among the constraint normals occurs at the solution or in some other region.
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References
Powell, M. J. D.,A Fast Algorithm for Nonlinearly Constrained Optimization Calculations, Paper Presented at the Conference on Numerical Analysis, Dundee, Scotland, 1977.
Bartholomew-Biggs, M. C.,Recursive Quadratic Programming Based on Penalty Functions for Constrained Minimization, Nonlinear Optimization Theory and Algorithms, Edited by L. C. W. Dixon, E. Spedicato, and G. P. Szegö, Birkhauser Books, Boston, Massachusetts, 1980.
Bartholomew-Biggs, M. C.,Recursive Quadratic Programming Methods for Nonlinear Constraints, Nonlinear Optimization 1981, Edited by M. J. D. Powell, Academic Press, New York, New York, 1981.
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Communicated by L. C. W. Dixon
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Bartholomew-Biggs, M.C. Numerical examples of the behavior of REQP on nonlinear programming problems involving linear dependence among the constraint normals. J Optim Theory Appl 48, 215–227 (1986). https://doi.org/10.1007/BF00940670
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DOI: https://doi.org/10.1007/BF00940670