Low-sum order value optimization / Otimização da menor soma de valores ordenados
AUTOR(ES)
Flavio Sakakisbara Yano
DATA DE PUBLICAÇÃO
2006
RESUMO
Given r real functions Fl(X),..., Fr(x) defined in n c IRn 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 smallest values. If (Yl,..., Yr) is a vector of data and T(x, ti) is the predicted value of the i-th observation ith the parameters x E n, it is natural to define Fi(X) = (T(X,ti) -Yi)2 (the quadratic error at observation i under the parameters x). Vhen p = r this LaVO problem coincides with the classical nonlinear least-squares problem. However, the interesting situation is when p is smaller than r. In that case, the solution of LOVO allows one to discard the infiuence of an estimated number of outliers. Thus, the LaVO 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 work optimality conditions are discussed, algorithms for solving the LOVO problem are introduced and convergence theorems are proved. Finally, numerical experiments are presented
ASSUNTO(S)
programação não-linear otimização nonlinear programming estimativa de parametro parameter estimation optimization
