Summary: Nonlinear�Programming Reformulation of the
Order�Value Optimization problem #
Roberto Andreani + Cibele Dunder # Jos�e Mario Mart��nez �
April 22, 2004
Abstract
Order�value optimization (OVO) is a generalization of the min�
imax problem motivated by decision�making problems under uncer�
tainty and by robust estimation. New optimality conditions for this
nonsmooth optimization problem are derived. An equivalent mathe�
matical programming problem with equilibrium constraints is deduced.
The relation between OVO and this nonlinear�programming reformu�
lation is studied. Particular attention is given to the relation between
local minimizers and stationary points of both problems.
Keywords: Order�value optimization, optimality conditions, nonlinear�
programming, equilibrium constraints, optimization algorithms.
1 Introduction
Assume that f 1 , . . . , f m are real�valued functions defined on an arbitrary set
#. For each x # # the values f 1 (x), . . . , f m (x) are ordered in such a way
that
f i 1 (x) (x) # f i 2 (x) (x) # . . . # f i m (x) (x).

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

Collections: Mathematics