Journal of the Operations Research Society of Japan
Online ISSN : 2188-8299
Print ISSN : 0453-4514
A NOTE ON THE SQUARED SLACK VARIABLES TECHNIQUE FOR NONLINEAR OPTIMIZATION
Ellen H. FukudaMasao Fukushima
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2017 Volume 60 Issue 3 Pages 262-270

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Abstract

In constrained nonlinear optimization, the squared slack variables can be used to transform a problem with inequality constraints into a problem containing only equality constraints. This reformulation is usually not considered in the modern literature, mainly because of possible numerical instabilities. However, this argument only concerns the development of algorithms, and nothing stops us in using the strategy to understand the theory behind these optimization problems. In this note, we clarify the relation between the Karush-Kuhn-Tucker points of the original and the reformulated problems. In particular, we stress that the second-order sufficient condition is the key to establish their equivalence.

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© 2017 The Operations Research Society of Japan
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