In this paper, we introduce a class of generalized second order （F,α,ρ , d,p）-univex functions. Two types of second order dual models are considered for a minimax fractional programming problem and the duality res...In this paper, we introduce a class of generalized second order （F,α,ρ , d,p）-univex functions. Two types of second order dual models are considered for a minimax fractional programming problem and the duality results are established by using the assumptions on the functions involved.展开更多
This paper considers a nonsmooth semi-infinite minimax fractional programming problem(SIMFP)involving locally Lipschitz invex functions.The authors establish necessary optimality conditions for SIMFP.The authors estab...This paper considers a nonsmooth semi-infinite minimax fractional programming problem(SIMFP)involving locally Lipschitz invex functions.The authors establish necessary optimality conditions for SIMFP.The authors establish the relationship between an optimal solution of SIMFP and saddle point of scalar Lagrange function for SIMFP.Further,the authors study saddle point criteria of a vector Lagrange function defined for SIMFP.展开更多
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 No.11101016)
文摘In this paper, we introduce a class of generalized second order （F,α,ρ , d,p）-univex functions. Two types of second order dual models are considered for a minimax fractional programming problem and the duality results are established by using the assumptions on the functions involved.
基金supported by the Council of Scientific and Industrial Research(CSIR),New Delhi,India under Grant No.09/013(0474)/2012-EMR-1
文摘This paper considers a nonsmooth semi-infinite minimax fractional programming problem(SIMFP)involving locally Lipschitz invex functions.The authors establish necessary optimality conditions for SIMFP.The authors establish the relationship between an optimal solution of SIMFP and saddle point of scalar Lagrange function for SIMFP.Further,the authors study saddle point criteria of a vector Lagrange function defined for SIMFP.
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.
