uv-decomposition method for solving a mathematical program with equilibrium constraints （MPEC） problem with linear complementarity constraints is presented. The problem is first converted into a nonlinear programmin...uv-decomposition method for solving a mathematical program with equilibrium constraints （MPEC） problem with linear complementarity constraints is presented. The problem is first converted into a nonlinear programming one. The structure of subdifferential a corresponding penalty function and results of its uv-decomposition are given. A conceptual algorithm for solving this problem with a superUnear convergence rate is then constructed in terms of the obtained results.展开更多
An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programmin...An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programming with equilibrium constraints （MPEC）. The upper level of the MNDP aims to optimize the network performance via both the expansion of existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium （UE） model. The idea of the proposed DDIA is to reduce the dimensions of the problem. A group of variables （discrete/continuous） are fixed to altemately optimize another group of variables （continuous/discrete）. Some continuous network design problems （CNDPs） and discrete network design problems （DNDPs） are solved repeatedly until the optimal solution is obtained. A numerical example is given to demonstrate the efficiency of the proposed algorithm.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.10372063,10771026 and 10471015)
文摘uv-decomposition method for solving a mathematical program with equilibrium constraints （MPEC） problem with linear complementarity constraints is presented. The problem is first converted into a nonlinear programming one. The structure of subdifferential a corresponding penalty function and results of its uv-decomposition are given. A conceptual algorithm for solving this problem with a superUnear convergence rate is then constructed in terms of the obtained results.
基金The National Natural Science Foundation of China(No. 50908235 )China Postdoctoral Science Foundation (No.201003520)
文摘An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programming with equilibrium constraints （MPEC）. The upper level of the MNDP aims to optimize the network performance via both the expansion of existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium （UE） model. The idea of the proposed DDIA is to reduce the dimensions of the problem. A group of variables （discrete/continuous） are fixed to altemately optimize another group of variables （continuous/discrete）. Some continuous network design problems （CNDPs） and discrete network design problems （DNDPs） are solved repeatedly until the optimal solution is obtained. A numerical example is given to demonstrate the efficiency of the proposed algorithm.
