# A quadratic penalty algorithm for linear programming and its application to linearizations of quadratic assignment problems

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I. L. Galabova and J. A. J. Hall
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Abstract
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This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying algorithm is a penalty method with naive approximate minimization in each iteration. During initial iterations an approach similar to augmented Lagrangian is used. Later the technique corresponds closely to a classical quadratic penalty method. There is also a discussion of the extent to which it can be used to obtain fast approximate solutions of LP problems, in particular when applied to linearizations of quadratic assignment problems.

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Key words:
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Linear programming; quadratic penalty methods; quadratic assignment problems

**Text**

Technical report: ERGO-18-009

**History:**

Submitted to

*Optimization Methods and Software*

Also available via arXiv as goo.gl/cQKGgU

Also available via Optimization Online