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A note on the squared slack variables technique for nonlinear optimization

Ellen H. Fukuda(ellen***at***i.kyoto-u.ac.jp)
Masao Fukushima(fuku***at***nanzan-u.ac.jp)

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.

Keywords: Nonlinear programming, Karush-Kuhn-Tucker conditions, second-order sufficient condition, squared slack variables

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Kyoto University / Nanzan University, May 2016.

Download: [PDF]

Entry Submitted: 05/29/2016
Entry Accepted: 05/29/2016
Entry Last Modified: 05/29/2016

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