Displaying similar documents to “Remarks on the Newton method for solving nonlinear equality constrained optimization problems”

On diagonally-preconditioning the truncated-Newton method for super-scale linearly constrained nonlinear programming.

Laureano F. Escudero (1982)

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We present an algorithm for super-scale linearly constrained nonlinear programming (LCNP) based on Newton's method. In large scale programming solving Newton's equation at each iteration can be expensive and may not be justified when far from a local solution; we briefly review the current existing methodologies, such that by classifying the problems in small-scale, super-scale and supra-scale problems we suggest the methods that, based on our own computational experience, are more suitable...

On diagonally preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming.

Laureano F. Escudero (1982)

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We present an algorithm for supra-scale linearly constrained nonlinear programming (LNCP) based on the Limited-Storage Quasi-Newton's method. In large-scale programming solving the reduced Newton equation at each iteration can be expensive and may not be justified when far from a local solution; besides, the amount of storage required by the reduced Hessian matrix, and even the computing time for its Quasi-Newton approximation, may be prohibitive. An alternative based on the reduced...

On superlinear multiplier update methods for partial augmented Lagrangian techniques.

Eugenio Mijangos (2002)

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The minimization of a nonlinear function with linear and nonlinear constraints and simple bounds can be performed by minimizing an augmented Lagrangian function, including only the nonlinear constraints. This procedure is particularly interesting in case that the linear constraints are flow conservation equations, as there exist efficient techniques to solve nonlinear network problems. It is then necessary to estimate their multipliers, and variable reduction techniques can be used to...