1984 Reports

# Some Nonlinear Problems Are as Easy as the Approximation Problem

In this paper we study the following problem. Given an operator S and a subset F0 of some linear space, approximate S (f) for any f ∈ F0 possessing only partial information on f. Although all operators S considered here are nonlinear (e.g. min f(x). min|f(x) |. 1/f or ||f||, we prove that these problems are "equivalent" to the problem of approximating S(j)=f. i.e. S=I. This equivalence provides optimal (or nearly optimal) information and algorithms.

## Subjects

## Files

- cucs-148-84.pdf application/x-pdf 496 KB Download File

## More About This Work

- Academic Units
- Computer Science
- Publisher
- Department of Computer Science, Columbia University
- Series
- Columbia University Computer Science Technical Reports, CUCS-148-84
- Published Here
- February 23, 2012