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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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On secant updates for use in general constrained optimization
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by Richard Tapia PDF
Math. Comp. 51 (1988), 181-202 Request permission


In this paper we present two new classes of successive quadratic programming (SQP) secant methods for the equality-constrained optimization problem. One class of methods uses the SQP augmented Lagrangian formulation, while the other class uses the SQP Lagrangian formulation. We demonstrate, under the standard assumptions, that in both cases the BFGS and DFP versions of the algorithm are locally q-superlinearly convergent. To our knowledge this is the first time that either local or q-superlinear convergence has been established for an SQP Lagrangian secant method which uses either the BFGS or DFP updating philosophy and assumes no more than the standard assumptions. Since the standard assumptions do not require positive definiteness of the Hessian of the Lagrangian at the solution, it is no surprise that our BFGS and DFP updates possess the hereditary positive definiteness property only on a proper subspace.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Math. Comp. 51 (1988), 181-202
  • MSC: Primary 90C30; Secondary 49D37, 90C20
  • DOI:
  • MathSciNet review: 942149