Simplified Variants of Penalty Function Methods

Evtushenko, Y. (1975). Simplified Variants of Penalty Function Methods. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-75-012

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Abstract

Penalty function methods have several disadvantages. The main ones are as follows: (1) The methods are time-consuming. They~do require multiple solving of unconstrained minimization sub-problems; (2) Solution of minimization sub-problems becomes exceedingly cumbersome when the penalty coefficient increases, since a minimization function becomes ill-conditioned; (3) The usual penalty methods cannot be used for determining a solution with great accuracy. These methods are subject to numerical instabilities because the derivatives of the penalty functions increase without bound near the solution as computation proceeds. The methods suggested in this paper essentially simplify standard penalty function procedure and remove, to some extent, the first two shortcomings.

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