Newton’s method may fail to recognize proximity to optimal points in constrained optimization

We will show examples in which the primal sequence generated by the Newton–Lagrange method converges to a strict local minimizer of a constrained optimization problem but the gradient of the Lagrangian does not tend to zero, independently of the choice of the dual sequence.

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Bibliographic Details
Published in:Mathematical programming 2016-11, Vol.160 (1-2), p.547-555
Main Authors: Andreani, R., Martínez, J. M., Santos, L. T.
Format: Article
Language:English
Subjects:
Algorithms
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Lagrange multiplier
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Short Communication
Studies
Theoretical
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Description
Summary:We will show examples in which the primal sequence generated by the Newton–Lagrange method converges to a strict local minimizer of a constrained optimization problem but the gradient of the Lagrangian does not tend to zero, independently of the choice of the dual sequence.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-016-0994-6