Applied mathematics

On constructing exact penalty functions

Yu. P. Laptin

V. M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, 03650 Kiev, Ukraine

Abstract: There are a large number of publications dedicated to investigation and problems of using exact penalty functions. At present the method of exact penalty functions is widely used for solving optimization problems with constraints. But using this method involves certain difficulties. Particularly there are no simple techniques of calculating the acceptable values of penalty coefficients. The article discusses approaches to determine the value of penalty coefficients for convex problems during the execution of the optimization algorithm. Significant difficulties in forming the equivalent unconstrained optimization problems arise if the functions describing the original problem are not defined on the whole variable space. For such case it is proposed to use special extensions of functions from a feasible set of the original problem to the whole variable space. This approach also allows to overcome the problem of bad scalability of the original problem. Bibliogr. 9. Il. 1.

Keywords: nondifferentiable optimization, penalty functions, convex extension of functions.

UDC: 519.8

Received: May 30, 2013