In this paper, a new global algorithm is presented to globally solve the linear multiplicative programming（LMP）. The problem（LMP） is firstly converted into an equivalent programming problem（LMP（H））by introduci...In this paper, a new global algorithm is presented to globally solve the linear multiplicative programming（LMP）. The problem（LMP） is firstly converted into an equivalent programming problem（LMP（H））by introducing p auxiliary variables. Then by exploiting structure of（LMP（H））, a linear relaxation programming（LP（H）） of（LMP（H）） is obtained with a problem（LMP） reduced to a sequence of linear programming problems. The algorithm is used to compute the lower bounds called the branch and bound search by solving linear relaxation programming problems（LP（H））. The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.展开更多
A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not con...A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size, so providing the potential to dramatically improve the practical computation effectiveness.展开更多
基金Supported by the PhD Start-up Fund of Natural Science Foundation of Guangdong Province,China(No.S2013040012506)China Postdoctoral Science Foundation Funded Project(2014M562152)
文摘In this paper, a new global algorithm is presented to globally solve the linear multiplicative programming（LMP）. The problem（LMP） is firstly converted into an equivalent programming problem（LMP（H））by introducing p auxiliary variables. Then by exploiting structure of（LMP（H））, a linear relaxation programming（LP（H）） of（LMP（H）） is obtained with a problem（LMP） reduced to a sequence of linear programming problems. The algorithm is used to compute the lower bounds called the branch and bound search by solving linear relaxation programming problems（LP（H））. The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.
基金Supported by the Doctoral Educational Foundation of China of the Ministry of Education(20020486035)
文摘A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size, so providing the potential to dramatically improve the practical computation effectiveness.
