A projected Newton method in a Cartesian product of balls
type: Item
instance of: scholarly article
title: A projected Newton method in a Cartesian product of balls
zbMATH Open document ID: 0628.90063
DOI: 10.1007/BF00939866
author: B. George
published in: Journal of Optimization Theory and Applications
publication date: 1988-01-01T00:00:00Z
review text: We formulate a locally superlinearly convergent projected Newton method for constrained minimization in a Cartesian product of balls. For discrete-time, N-stage, input-constrained optimal control problems with Bolza objective functions, we then show how the required scaled tangential component of the objective function gradient can be approximated efficiently with a differential dynamic programming scheme; the computational cost and the storage requirements for the resulting modified projected Newton algorithm increase linearly with the number of stages. In calculations performed for a specific control problem with 10 stages, the modified projected Newton algorithm is shown to be one to two orders of magnitude more efficient than a standard unscaled projected gradient method.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49M37
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C39
zbMATH DE Number: 4023029
zbMATH Keywords: locally superlinearly convergent projected Newton method
zbMATH Keywords: constrained minimization
zbMATH Keywords: Cartesian product of balls
zbMATH Keywords: optimal control
zbMATH Keywords: Bolza objective functions
zbMATH Keywords: differential dynamic programming
MaRDI profile type: Publication
cites work: Projected Newton Methods for Optimization Problems with Simple Constraints
cites work: Two-Metric Projection Methods for Constrained Optimization
cites work: Newton-Goldstein convergence rates for convex constrained minimization problems with singular solutions
cites work: A class of superlinearly convergent projection algorithms with relaxed stepsizes
cites work: On the convergence of projected gradient processes to singular critical points
cites work: Variable metric gradient projection processes in convex feasible sets defined by nonlinear inequalities
cites work: Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms
cites work: Projected Hessian Updating Algorithms for Nonlinearly Constrained Optimization
full work available at URL: https://doi.org/10.1007/bf00939866
OpenAlex ID: W2080299905
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description: scientific article; zbMATH DE number 4023029