In this paper,we study the minimax linear fractional programming problem on a non-empty bounded set,called problem(MLFP),and we design a branch and bound algorithm to find a globally optimal solution of(MLFP).Firstly,...In this paper,we study the minimax linear fractional programming problem on a non-empty bounded set,called problem(MLFP),and we design a branch and bound algorithm to find a globally optimal solution of(MLFP).Firstly,we convert the problem(MLFP)to a problem(EP2)that is equivalent to it.Secondly,by applying the convex relaxation technique to problem(EP2),a convex quadratic relaxation problem(CQRP)is obtained.Then,the overall framework of the algorithm is given and its convergence is proved,the worst-case iteration number is also estimated.Finally,experimental data are listed to illustrate the effectiveness of the algorithm.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.12071133 and 11871196).
文摘In this paper,we study the minimax linear fractional programming problem on a non-empty bounded set,called problem(MLFP),and we design a branch and bound algorithm to find a globally optimal solution of(MLFP).Firstly,we convert the problem(MLFP)to a problem(EP2)that is equivalent to it.Secondly,by applying the convex relaxation technique to problem(EP2),a convex quadratic relaxation problem(CQRP)is obtained.Then,the overall framework of the algorithm is given and its convergence is proved,the worst-case iteration number is also estimated.Finally,experimental data are listed to illustrate the effectiveness of the algorithm.
基金Supported by the National Natural Science Foundation of China(10671057)Natural Science Foundation of Henan Institute of Science and Technology(06054 ,06055)
基金Supported by the National Natural Science Foundation of China (11171094)the Doctor Scientific Research Foundation of Henan Normal University (QD12103)
基金Supported by the National Natural Science Foundation of China(11171094)the Key Scientific and Technological Project of Henan Province(142102210058)+3 种基金the Doctoral Scientific Research Foundation of Henan Normal University(qd12103)the Youth Science Foundation of Henan Normal University(2013qk02)the Henan Normal University national research project to cultivate the Funded Projects(01016400105)the Henan Normal University Youth Backbone Teacher Training
基金Supported by the Basic and Advanced Technology Research Project of Henan Province(152300410097)the Science and Technology Key Project of Education Department of Henan Province(14A110024,16A110014)the Major Scientific Research Projects of Henan Institute of Science and Technology(2015ZD07)
