Summary: NonlinearProgramming Reformulation of the
OrderValue Optimization problem #
Roberto Andreani + Cibele Dunder # Jose Mario Martnez §
April 22, 2004
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.
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
f i 1 (x) (x) # f i 2 (x) (x) # . . . # f i m (x) (x).