This note considers possible arrangements of the sectors of a generalised dartboard. The sum of the pth powers of the absolute differences of the numbers on adjacent sectors is introduced as a penalty cost function and a string reversal algorithm is used to determine all arrangements that maximise the penalty, for any p ≥ 1. The maximum value of the penalty function for p = 1 is well known in t...

In this note we derive a geometric formulation for equality constrained problems of an ideal penalty function This di erentiable penalty function requires no parameter esti mation or adjustment has numerical conditioning similar to that of the target function from which it is constructed and also has the desirable property that the strict second order constrained minima of the target function a...

This paper presents an analysis of the involvement of the penalty parameter in exact penalty function methods that yields modiications to the standard outer loop which decreases the penalty parameter (typically dividing it by a constant). The procedure presented is based on the simple idea of making explicit the dependence of the penalty function upon the penalty parameter and is illustrated on...