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NonlinearProgramming Reformulation of the OrderValue Optimization problem #
 

Summary: Nonlinear­Programming Reformulation of the
Order­Value Optimization problem #
Roberto Andreani + Cibele Dunder # Jos’e Mario Mart’nez §
April 22, 2004
Abstract
Order­value optimization (OVO) is a generalization of the min­
imax problem motivated by decision­making 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 nonlinear­programming reformu­
lation is studied. Particular attention is given to the relation between
local minimizers and stationary points of both problems.
Keywords: Order­value optimization, optimality conditions, nonlinear­
programming, equilibrium constraints, optimization algorithms.
1 Introduction
Assume that f 1 , . . . , f m are real­valued 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 Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas

 

Collections: Mathematics