TY - JOUR
T1 - A min-max algorithm for non-linear regression models
AU - Tishler, A.
AU - Zang, I.
N1 - Funding Information:
Note added in proojI This research was carried out while A. Tishler was visiting at the Economics department, at the University of Southern California, and I. Zang was visiting at the Faculty of Commerce and Business Administration, the University of British Columbia. Research was partially supported by the Israel Institute of Business Research at Tel-Aviv University.
PY - 1983/8
Y1 - 1983/8
N2 - We present a simple method for the nonlinear min-max (or L∞) estimation problem. The method consists of locally smoothing out the nondifferentiabilities in the original L∞ problem, resulting in an approximate differentiable one that can be estimated using standard gradient techniques. The accuracy of the approximation is determined by a single parameter, whose choice determines a priori the length of the uncertainty interval in the maximal absolute error for the solution of the original L∞ problem. In addition, we present some numerical examples demonstrating the efficiency of the method.
AB - We present a simple method for the nonlinear min-max (or L∞) estimation problem. The method consists of locally smoothing out the nondifferentiabilities in the original L∞ problem, resulting in an approximate differentiable one that can be estimated using standard gradient techniques. The accuracy of the approximation is determined by a single parameter, whose choice determines a priori the length of the uncertainty interval in the maximal absolute error for the solution of the original L∞ problem. In addition, we present some numerical examples demonstrating the efficiency of the method.
UR - http://www.scopus.com/inward/record.url?scp=48749149758&partnerID=8YFLogxK
U2 - 10.1016/0096-3003(83)90032-2
DO - 10.1016/0096-3003(83)90032-2
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AN - SCOPUS:48749149758
SN - 0096-3003
VL - 13
SP - 95
EP - 115
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 1-2
ER -