On the Location of Directions of Infinite Descent for Nonlinear Programming Algorithms

There is much current interest in general equality constrained quadratic programming problems, both for their own sake and for their applicability to active set methods for nonlinear programming. In the former case, typically, the issues are existence of solutions and their determination. In the lat...

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Bibliographic Details
Published in:SIAM journal on numerical analysis Vol. 21; no. 6; pp. 1162 - 1179
Main Authors: Conn, Andrew R., Nicholas I. M. Gould
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.12.1984
Subjects:
Algorithms
Applied sciences
Cholesky factorization
Curvature
Eigenvalues
Exact sciences and technology
Factorization
Lagrangian function
Mathematical programming
Mathematical vectors
Matrices
Methods
Nonlinear programming
Operational research and scientific management
Operational research. Management science
Quadratic programming
Scalars
Non linear programming
Quadratic programming
Algorithm
Constrained optimization
Mathematical programming
ISSN:0036-1429, 1095-7170
Online Access:Get full text
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Summary:There is much current interest in general equality constrained quadratic programming problems, both for their own sake and for their applicability to active set methods for nonlinear programming. In the former case, typically, the issues are existence of solutions and their determination. In the latter instance, nonexistence of solutions gives rise to directions of infinite descent. Such directions may subsequently be used to determine a more desirable active set. The generalised Cholesky decomposition of relevant matrices enables us to answer the question of existence and to determine directions of infinite descent (when applicable) in an efficient and stable manner. The methods examined are related to implementations that are suitable for null-space, range-space and Lagrangian methods.
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ISSN:0036-1429
1095-7170
DOI:10.1137/0721072