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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 descr ..."
Abstract

Cited by 74 (11 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.
On the Use of ElementbyElement Preconditioners to Solve Large Scale Partially Separable Optimization Problems
"... We study the solution of largescale nonlinear optimization problems by methods which aim to exploit their inherent structure. In particular, we consider the allpervasive property of partial separability, first studied by Griewank and Toint (1982b). A typical minimizationmethod for nonlinear optimi ..."
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Cited by 8 (5 self)
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We study the solution of largescale nonlinear optimization problems by methods which aim to exploit their inherent structure. In particular, we consider the allpervasive property of partial separability, first studied by Griewank and Toint (1982b). A typical minimizationmethod for nonlinear optimization problems approximately solves a sequence of simplified linearized subproblems. In this paper, we explore how partial separability may be exploited by iterative methods for solving these subproblems. We particularly address the issue of computing effective preconditioners for such iterative methods. Numerical experiments indicate the effectiveness of these preconditioners on largescale examples. Keywords: largescale problems, unconstrained optimization, elememtbyelement preconditioners, conjugategradients. AMS(MOS) subject classifications: 65F05, 65F10, 65F15, 65F50, 65K05, 90C30. Also appeared as ENSEEIHTIRIT report RT/APO/94/4. 1 Travel was funded, in part, by the ALLIANCE...
NorthHolland Publishing Company MATRIX FACTOR1ZATIONS IN OPTIMIZATION OF NON LINEAR FUNCTIONS SUBJECT TO LINEAR CONSTRAINTS*
, 1974
"... Several ways of implementing methods for solving nonlinear optimization problems involving linear inequality and equality constraints using numerically stable matrix factorizations are described. The methods considered all follow an active constraint set approach and include quadratic programming, v ..."
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Several ways of implementing methods for solving nonlinear optimization problems involving linear inequality and equality constraints using numerically stable matrix factorizations are described. The methods considered all follow an active constraint set approach and include quadratic programming, variable metric, and modified Newton methods. 1.
NorthHolland Publishing Company A DISCRETE NEWTON ALGORITHM A FUNCTION OF MANY VARIABLES FOR MINIMIZING
, 1980
"... A Newtonlike method is presented for minimizing a function of n variables. It uses only function and gradient values and is a variant of the discrete Newton algorithm. This variant requires fewer operations than the standard method when n> 39, and storage is proportional to n rather than n 2. ..."
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A Newtonlike method is presented for minimizing a function of n variables. It uses only function and gradient values and is a variant of the discrete Newton algorithm. This variant requires fewer operations than the standard method when n> 39, and storage is proportional to n rather than n 2.