In this paper,we investigate dual problems for nonconvex set-valued vector optimization via abstract subdifferential.We first introduce a generalized augmented Lagrangian function induced by a coupling vector-valued f...In this paper,we investigate dual problems for nonconvex set-valued vector optimization via abstract subdifferential.We first introduce a generalized augmented Lagrangian function induced by a coupling vector-valued function for set-valued vector optimization problem and construct related set-valued dual map and dual optimization problem on the basic of weak efficiency,which used by the concepts of supremum and infimum of a set.We then establish the weak and strong duality results under this augmented Lagrangian and present sufficient conditions for exact penalization via an abstract subdifferential of the object map.Finally,we define the sub-optimal path related to the dual problem and show that every cluster point of this sub-optimal path is a primal optimal solution of the object optimization problem.In addition,we consider a generalized vector variational inequality as an application of abstract subdifferential.展开更多
Rolling planning is an efficient method for path planning in uncertain environment. In this paper, the general principle and algorithm of mobile robot path planning based on rolling windows are studied. The sub-optim... Rolling planning is an efficient method for path planning in uncertain environment. In this paper, the general principle and algorithm of mobile robot path planning based on rolling windows are studied. The sub-optimality of rolling path planning is analyzed in details and explained with a concrete example.展开更多
基金supported by National Science Foundation of China(No.11401487)the Education Department of Shaanxi Province(No.17JK0330)+1 种基金the Fundamental Research Funds for the Central Universities(No.300102341101)State Key Laboratory of Rail Transit Engineering Informatization(No.211934210083)。
文摘In this paper,we investigate dual problems for nonconvex set-valued vector optimization via abstract subdifferential.We first introduce a generalized augmented Lagrangian function induced by a coupling vector-valued function for set-valued vector optimization problem and construct related set-valued dual map and dual optimization problem on the basic of weak efficiency,which used by the concepts of supremum and infimum of a set.We then establish the weak and strong duality results under this augmented Lagrangian and present sufficient conditions for exact penalization via an abstract subdifferential of the object map.Finally,we define the sub-optimal path related to the dual problem and show that every cluster point of this sub-optimal path is a primal optimal solution of the object optimization problem.In addition,we consider a generalized vector variational inequality as an application of abstract subdifferential.
基金This work was supported by the National 973 Plan (Grant No. G1998030415)the National Natural Science Foundation of China (Grant No. 69934020)the National 863 Program (Grant No. 2001AA422140).
文摘 Rolling planning is an efficient method for path planning in uncertain environment. In this paper, the general principle and algorithm of mobile robot path planning based on rolling windows are studied. The sub-optimality of rolling path planning is analyzed in details and explained with a concrete example.
