Nonlinear optimization and approximation

fragmentability and approximation

in chapter 1, charactrizations of fragmentability, which are obtained by namioka (37), ribarska (45) and kenderov-moors (32), are given. also the connection between fragmentability and its variants and other topics in banach spaces such as analytic space, the radone-nikodym property, differentiability of convex functions, kadec renorming are discussed. in chapter 2, we use game characterization...

Nonlinear approximation

This is a survey of nonlinear approximation, especially that part of the subject which is important in numerical computation. Nonlinear approximation means that the approximants do not come from linear spaces but rather from nonlinear manifolds. The central question to be studied is what, if any, are the advantages of nonlinear approximation over the simpler, more established, linear methods. T...

Nonlinear approximation and its applications

I first met Wolfgang Dahmen in 1974 in Oberwolfach. He looked like a high school student to me but he impressed everyone with his talk on whether polynomial operators could produce both polynomial and spectral orders of approximation. We became the best of friends and frequent collaborators. While Wolfgang’s mathematical contributions spread across many disciplines, a major thread in his work h...

Nonlinear Approximation and the Space

Given a function f 2 L2(Q), Q := [0, 1)2 and a real number t > 0, let U( f , t) := infg2BV (Q) kf gkL2(I) + t VQ (g), where the infimum is taken over all functions g 2 BV of bounded variation on I. This and related extremal problems arise in several areas of mathematics such as interpolation of operators and statistical estimation, as well as in digital image processing. Techniques for finding ...

Nonlinear Methods of Approximation