 
Summary: Low OrderValue Optimization and applications
R. Andreani
J. M. Mart´inez
L. Mart´inez §
F. Yano ¶
October 24, 2005
Abstract
Given r real functions F1(x), . . . , Fr(x) and an integer p between 1 and r, the Low Order
Value Optimization problem (LOVO) consists of minimizing the sum of the functions that
take the p smaller values. If (y1, . . . , yr) is a vector of data and T(x, ti) is the predicted
value of the observation i with the parameters x IRn
, it is natural to define Fi(x) =
(T(x, ti)  yi)2
(the quadratic error at observation i under the parameters x). When p = r
this LOVO problem coincides with the classical nonlinear leastsquares problem. However,
the interesting situation is when p is smaller than r. In that case, the solution of LOVO allows
one to discard the influence of an estimated number of outliers. Thus, the LOVO problem is
an interesting tool for robust estimation of parameters of nonlinear models. When p << r
the LOVO problem may be used to find hidden structures in data sets.
In this paper optimality conditions are discussed, algorithms for solving the LOVO prob
