Summary: Order�Value Optimization: Formulation and
Solution by means of a Primal Cauchy Method
Roberto Andreani # Cibele Dunder + Jos�e Mario Mart��nez #
December 19, 2002
Abstract
The Order�Value Optimization (OVO) problem is a generalization
of the classical Minimax problem. Instead of the maximum of a set
functions, the functional value that ranks in the p-th place is mini�
mized. The problem seeks the application to (non�pessimistic) decision
making and to model fitting in the presence of (perhaps systematic)
outliers. A Cauchy�type method is introduced that solves the prob�
lem in the sense that every limit point satisfies an adequate optimality
condition. Numerical examples are given.
Key words: Order�Value Optimization, iterative methods, global
convergence, fitting parameters.
1 Introduction
Given m functions f 1 , . . . , f m , defined in a
domain# # IR n and an integer
p # {1, . . . , m}, the (p-) Order�Value (OVO) function f is given by
f(x) = f i p (x) (x),

Source: Andreani, Roberto - Instituto de Matem�tica, Estat�stica e Computa��o Cient�fica, Universidade Estadual de Campinas

Collections: Mathematics