Research on the method for interval linear bi-level programming based on a partial order on intervals

Satisfactory solutions of interval programming and interval linear bi-level programming are defined based on a new partial order on intervals. The optimality condition for interval programming is investigated. Based on K-T optimality condition, satisfactory solution of interval linear bi-level programming is obtained from a bi-objective programming. Finally, a numerical example is presented.

[1]  Tong Shaocheng,et al.  Interval number and fuzzy number linear programmings , 1994 .

[2]  Jonathan F. Bard,et al.  Practical Bilevel Optimization , 1998 .

[3]  Ding Chaoyua,et al.  Notes to interval number linear programming and its satisfactory solution , 2003 .

[4]  Debjani Chakraborty,et al.  Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming , 2001, Fuzzy Sets Syst..

[5]  Yozo Nakahara,et al.  On the linear programming problems with interval coefficients , 1992 .

[6]  Shiang-Tai Liu,et al.  A numerical solution method to interval quadratic programming , 2007, Appl. Math. Comput..

[7]  E. Aiyoshi,et al.  Necessary conditions for min-max problems and algorithms by a relaxation procedure , 1980 .

[8]  Jonathan F. Bard,et al.  Practical Bilevel Optimization: Algorithms and Applications , 1998 .

[9]  Guo Jun-peng.  Standard form of interval linear programming and its optimal objective (interval value) , 2004 .

[10]  Masahiro Inuiguchi,et al.  Minimax regret solution to linear programming problems with an interval objective function , 1995 .

[11]  Heinrich von Stackelberg,et al.  Stackelberg (Heinrich von) - The Theory of the Market Economy, translated from the German and with an introduction by Alan T. PEACOCK. , 1953 .

[12]  M. Patriksson,et al.  Stochastic bilevel programming in structural optimization , 2001 .

[13]  Wei Li,et al.  Numerical solution method for general interval quadratic programming , 2008, Appl. Math. Comput..

[14]  Manuel Laguna,et al.  Theory and Methodology A heuristic to minimax absolute regret for linear programs with interval objective function coeÅcients , 1999 .

[15]  Jie Lu,et al.  Fuzzy bilevel programming with multiple objectives and cooperative multiple followers , 2010, J. Glob. Optim..

[16]  Xiong Wen-tao.  A New Solution for Interval Number Linear Programming , 2005 .

[17]  M. Inuiguchi,et al.  Goal programming problems with interval coefficients and target intervals , 1991 .