Browsing by Author "Molla, Abay"

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    A Multiparametric Programming Approach for Multilevel Optimization
    (Addis Ababa, Ethiopia, 2011) Molla, Abay; Mitiku, Semu (PhD)
    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