Approximation scheme for functional optimization problems

Approximation schemes for functional optimization problems with admissible solutions dependent on a large number d of variables are investigated. Suboptimal solutions are considered, expressed as linear combinations of n-tuples from a basis set of simple computational units with adjustable parameters. Different choices of basis sets are compared, which allow one to obtain suboptimal solutions using a number n of basis functions that does not grow \u201cfast\u201d with the number d of variables in the admissible decision functions for a fixed desired accuracy. In these cases, one mitigates the \u201ccurse of dimensionality,\u201d which often makes unfeasible traditional linear approximation techniques for functional optimization problems, when admissible solutions depend on a large number d of variables