A new system of generalized mixed equilibrium problems （SGMEPs） involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalize...A new system of generalized mixed equilibrium problems （SGMEPs） involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalized mixed equilibrium problems （SAGMEPs） for solving the SGMEPs is first introduced. Existence and uniqueness of the solutions to the SAGMEPs is proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Using the auxiliary principle technique, a new iterative algorithm for solving the SGMEPs is proposed and analyzed. Strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild assumptions without any coercive conditions. These results improve, unify, and generalize some recent results in this field.展开更多
A new bilevel generalized mixed equilibrium problem （BGMEP） involving generalized mixed variational-like inequality problems （GMVLIPs） is introduced and studied in the reflexive Banach spaces. First, an auxiliary ...A new bilevel generalized mixed equilibrium problem （BGMEP） involving generalized mixed variational-like inequality problems （GMVLIPs） is introduced and studied in the reflexive Banach spaces. First, an auxiliary generalized mixed equilibrium problem （AGMEP） is introduced to compute the approximate solutions of the BGMEP involving the GMVLIPs. By using a minimax inequality, the existence and the unique- ness of solutions of the AGMEP are proved under mild conditions without any coercive assumptions. By using an auxiliary principle technique, the new iterative algorithms are proposed and analyzed, with which the approximate solutions of the BGMEP are computed. The strong convergence of the iterative sequence generated by the algorithms is shown under mild conditions without any coercive assumptions. These new results can generalize some recent results in this field.展开更多
A system of generalized mixed equilibrium-like problems is introduced and the existence of its solutions is shown by using the auxiliary principle technique in Hilbert spaces.
随着电网规模的扩大,电网计算优化问题中计算时间长、收敛速度慢等问题变得严重。针对此问题,该文利用基于电网分区和辅助问题原理APP(Auxiliary Prob lem Princ ip le)的分布式并行优化模型来解决多区域有功负荷的经济调度,并且把各个...随着电网规模的扩大,电网计算优化问题中计算时间长、收敛速度慢等问题变得严重。针对此问题,该文利用基于电网分区和辅助问题原理APP(Auxiliary Prob lem Princ ip le)的分布式并行优化模型来解决多区域有功负荷的经济调度,并且把各个区域内的虚拟发电机看成真实发电机,推导出其耗量特性曲线。仿真结果表明,本方法具有较强的收敛性和快速性。展开更多
基金supported by the Scientific Research Fund of Sichuan Normal University (No.09ZDL04)the Sichuan Province Leading Academic Discipline Project (No.SZD0406)
文摘A new system of generalized mixed equilibrium problems （SGMEPs） involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalized mixed equilibrium problems （SAGMEPs） for solving the SGMEPs is first introduced. Existence and uniqueness of the solutions to the SAGMEPs is proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Using the auxiliary principle technique, a new iterative algorithm for solving the SGMEPs is proposed and analyzed. Strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild assumptions without any coercive conditions. These results improve, unify, and generalize some recent results in this field.
基金Project supported by the Scientific Research Fund of Sichuan Normal University(No.09ZDL04)the Leading Academic Discipline Project of Sichuan Province of China(No.SZD0406)
文摘A new bilevel generalized mixed equilibrium problem （BGMEP） involving generalized mixed variational-like inequality problems （GMVLIPs） is introduced and studied in the reflexive Banach spaces. First, an auxiliary generalized mixed equilibrium problem （AGMEP） is introduced to compute the approximate solutions of the BGMEP involving the GMVLIPs. By using a minimax inequality, the existence and the unique- ness of solutions of the AGMEP are proved under mild conditions without any coercive assumptions. By using an auxiliary principle technique, the new iterative algorithms are proposed and analyzed, with which the approximate solutions of the BGMEP are computed. The strong convergence of the iterative sequence generated by the algorithms is shown under mild conditions without any coercive assumptions. These new results can generalize some recent results in this field.
文摘A system of generalized mixed equilibrium-like problems is introduced and the existence of its solutions is shown by using the auxiliary principle technique in Hilbert spaces.
文摘随着电网规模的扩大,电网计算优化问题中计算时间长、收敛速度慢等问题变得严重。针对此问题,该文利用基于电网分区和辅助问题原理APP(Auxiliary Prob lem Princ ip le)的分布式并行优化模型来解决多区域有功负荷的经济调度,并且把各个区域内的虚拟发电机看成真实发电机,推导出其耗量特性曲线。仿真结果表明,本方法具有较强的收敛性和快速性。
