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This paper provides the first meaningful documentation and analysis of anestablished technique which aims to obtain an approximate solution to linearprogramming problems prior to applying the primal simplex method. Theunderlying algorithm is a penalty method with naive approximate minimization ineach iteration. During initial iterations an approach similar to augmentedLagrangian is used. Later the technique corresponds closely to a classicalquadratic penalty method. There is also a discussion of the extent to which itcan be used to obtain fast approximate solutions of LP problems, in particularwhen applied to linearizations of quadratic assignment problems.

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