Some nonlinear problems are as easy as the approximation problem

✍ Scribed by G.W. Wasilkowski

• Publisher: Elsevier Science
• Year: 1984
• Tongue: English
• Weight: 775 KB
• Volume: 10
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(84)90063-4

✦ Synopsis

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 fEF, possessing only partial .information on f. Although all operators S considered here are nonlinear (e.g. min f(x), minlf(x)j, l/f or [Ml), we prove that these problems are "equivalent" to the problem of approximating SCf)=f, i.e. S=I. This equivalence provides optimal (or nearly optimal) information and algorithms.