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Some Nonlinear Operators Are as Easy to Approximate as the Identity Operator

Department of Computer Science, Columbia University
Publication Date
  • Computer Science
  • Applied Mathematics
  • Computer Science


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

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