 
Summary: OrderValue 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 OrderValue 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 pth place is mini
mized. The problem seeks the application to (nonpessimistic) decision
making and to model fitting in the presence of (perhaps systematic)
outliers. A Cauchytype 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: OrderValue 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) OrderValue (OVO) function f is given by
f(x) = f i p (x) (x),
