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A class of accelerated conjugate direction methods for linearly constrained minimization problems


Authors: Michael J. Best and Klaus Ritter
Journal: Math. Comp. 30 (1976), 478-504
MSC: Primary 65K05; Secondary 90C30
DOI: https://doi.org/10.1090/S0025-5718-1976-0431675-3
MathSciNet review: 0431675
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Abstract: A class of algorithms are described for the minimization of a function of n variables subject to linear inequality constraints. Under weak conditions convergence to a stationary point is demonstrated. The method uses a mixture of conjugate direction constructing and accelerating steps. Any mixture, for example alternation, may be used provided that the subsequence of conjugate direction constructing steps is infinite. The mixture of steps may be specified so that under appropriate assumptions the rate of convergence of the method is two-step superlinear or $ (n - p + 1)$-step cubic where p is the number of constraints active at a stationary point. The accelerating step is always superlinearly convergent. A condition is given under which the alternating policy is every step superlinear. Computational results are given for several test problems.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1976-0431675-3
Keywords: Conjugate direction methods, superlinear convergence, mathematical programming, linearly constrained optimization
Article copyright: © Copyright 1976 American Mathematical Society