Dynamic programming and penalty functions

Penalty Functions for Genetic Programming Algorithms

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...

Exact Penalty Functions for Nonlinear Integer Programming Problems

Abstract In this work, we study exact continuous reformulations of nonlinear integer programming problems. To this aim, we preliminarily state conditions to guarantee the equivalence between pairs of general nonlinear problems. Then, we prove that optimal solutions of a nonlinear integer programming problem can be obtained by using various exact penalty formulations of the original problem in a...

Penalty Functions

Dynamic Programming with Homogeneous Functions

A major limitation in applying the tools of dynamic programming to many economic problems has been the lack of a general theory for the case where returns are unbounded. Except for a few special cases where closed form solutions are available (linear-quadratic models and the log-Cobb Douglas growth model being the leading examples), recursive methods have not been useful. Here we establish that...

Restricted dissimilarity functions and penalty functions

In this work we introduce the definition of restricted dissimilarity functions and we link it with some other notions, such as metrics. In particular, we also show how restricted dissimilarity functions can be used to build penalty functions.