Likelihood-based estimators with conventional regularization methods generally produces images with nonuniform and anisotropic spatial resolution properties. Previous work on penalty design for penalizedlikelihood estimators has led to statistical reconstruction methods that yield approximately uniform “average” resolution. However some asymmetries in the local point-spread functions persist. S...

The purposeof this paper is twofold. First we considera class of nondiierentiablepenaltyfunctions for constrained Lipschitz programs and then we show how these penalty functions can be employed to actually solve a constrained Lipschitz program. The penalty functions considered incorporate a barrier term which makes their value go to innnity on the boundary of a perturbation of the feasible set....

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve thi...

Constrained optimization via the Genetic Algorithm (GA) is often a challenging endeavor, as the GA is most directly suited to unconstrained optimization. Traditionally, external penalty functions have been used to convert a constrained optimization problem into an unconstrained problem for GA-based optimization. This approach requires the somewhat arbitrary selection of penalty draw-down coeffi...

We shall assume that each problem function has sufficiently many continuous derivatives for any implicit assumptions that we make to hold. One of the most successful tools for solving problems of the form NLP and SIP is the penalty function. A penalty-function approach replaces the relevant problem by a suitably weighted combination of the objective function f(x) and functions representing viol...

Mathematical measures of entropy as defined by Shannon (1948) and Kullback and Leibler (1951) are currently in vogue in the field of econometrics, primarily due to the comprehensive work by Golan, Judge, and Miller (1996). In this paper, an alternative interpretation of the entropy measure as a penalty function over deviations is presented. Using this interpretation, a number of parallels are d...

Very often symbolic regression, as addressed in Genetic Programming (GP), is equivalent to approximate interpolation. This means that, in general, GP algorithms try to fit the sample as better as possible but no notion of generalization error is considered. As a consequence, overfitting, code-bloat and noisy data are problems which are not satisfactorily solved under this approach. Motivated by...