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LARGESCALE LINEARLY CONSTRAINED OPTIMIZATION
, 1978
"... An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is ..."
Abstract

Cited by 93 (15 self)
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An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is described, along with computational experience on a wide variety of problems.
A new method to compute second derivatives
, 2001
"... In thisarticle we consider the problem of computing approximations to the second derivatives of functions of n variables using finite differences. We show how to derive different formulas and how to comput the errors of those approximations as functions of the increment h, both for first and second ..."
Abstract
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In thisarticle we consider the problem of computing approximations to the second derivatives of functions of n variables using finite differences. We show how to derive different formulas and how to comput the errors of those approximations as functions of the increment h, both for first and second derivatives. Based upon those results we describe the methods of Gill and Murray and the one of gradient difference. On the other hand we introduce a new algorithm which use conjugate directions methods for minimizing functions without derivatives and the corresponding numerical comparisons with the other two methods. Finally, numerical experiences are given and the corresponding conclusions are discussed.