Parametric global optimisation for bilevel programming

作     者：Faisca, Nuno P. Dua, Vivek Rustem, Berc Saraiva, Pedro M. Pistikopoulos, Efstratios N. 

作者机构：Imperial Coll London Ctr Proc Syst Engn London SW7 2AZ England UCL Ctr Proc Syst Engn London WC1E 7JE England Univ Coimbra Dept Chem Engn Gepsi PSE Grp P-3030290 Coimbra Portugal 

出 版 物：《JOURNAL OF GLOBAL OPTIMIZATION》 

年 卷 期：2007年第38卷第4期

页      面：609-623页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：bilevel programming parametric programming quadratic mixed-integer uncertainty 

摘      要：We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower s) problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables of the outer (leader s) problem. By inserting the obtained rational reaction sets in the upper level problem the overall problem is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global optimisation strategy.