A Multiparametric Programming Approach for Multilevel Optimization
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Date
2011
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Addis Ababa, Ethiopia
Abstract
Multilev I optimiza ion probl m ar math matical program which hav a sub t of th ir
variabl on train d to be an optimal oluti n of other program parameteriz d by their
r maining variabl s. It i implicitly d termined by a n of optimization probl m which
mu t b olved in a pred termin d qu n . T b mor precis , th inn r lev I probl m
i a multiparametri programming probl m param terized b upp I' I v I optimization
variable. The olution approa h for mul til v I programming problem i to repre nt
the inn r lev ,I problem with ufficient condi tion and a ugment it in the upper level constraints.
As a result , without convexity assumption for multilevel optimization at inn r
lev 1 , tationary point may not be su ffi cient or optimal for the inner I vel problem
and the set of all stationa ry point may not be connected. This impli s it is impossible
to usc the approach of augmenting the conditions of the lower level problem into the
constraints of th upper level problem. Recently, researchers have propo ed a olution
t rategy for multilevel optimization via multiparametric programming approach by conide
ring the follow r 's problem as a multiparamet ric optimization problem. But, their
propo ed algorithm work only for problem wi h convex , quadra tic or linear problem .
In this work , we pres nt the foundations of a gen ral global optimization algorithm for
the olu tion of general multilevel problem based on the r cent development in multiparametric
programming th ory. Specifically, we outline the general global optimization
stra t gy for the olu tion of bilevel and tril vel programming problem with nonconvexit
f rmulation at th inn l' I vel and w hav proved [-conv rgence of the algorithm
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Keywords
Multiparam tric programming, Mult il v I optimizat ion