A Geometric Approach to Fletcher's Ideal Penalty Function

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 are precisely those strict second order unconstrained minima of the penalty function which satisfy the constraints Such penalty functions can be used to establish termination properties for algorithms which avoid ill conditioned steps Numerical values for the penalty function and its derivatives can be e ciently calculated using automatic di erentiation techniques