The necessary condition established in Part I of this paper for the global maximizers of the maximization problem max V tr（VTAV）/tr（VTBV）＋tr（VTCV）over the Stiefel manifold{V∈Rm×l ｜VTV=Il}（l〈m）,natural...The necessary condition established in Part I of this paper for the global maximizers of the maximization problem max V tr（VTAV）/tr（VTBV）＋tr（VTCV）over the Stiefel manifold{V∈Rm×l ｜VTV=Il}（l〈m）,naturally leads to a self-consistent-field（SCF）iteration for computing a maximizer.In this part,we analyze the global and local convergence of the SCF iteration,and show that the necessary condition for the global maximizers is fulfilled at any convergent point of the sequences of approximations generated by the SCF iteration.This is one of the advantages of the SCF iteration over optimization-based methods.Preliminary numerical tests are reported and show that the SCF iteration is very efficient by comparing with some manifold-based optimization methods.展开更多
In this paper, on-road trajectory planning is solved by introducing intelligent computing budget allocation(ICBA) into a candidate-curve-based planning algorithm, namely, ordinal-optimization-based differential evolut...In this paper, on-road trajectory planning is solved by introducing intelligent computing budget allocation(ICBA) into a candidate-curve-based planning algorithm, namely, ordinal-optimization-based differential evolution(OODE). The proposed algorithm is named IOODE with ‘I' representing ICBA. OODE plans the trajectory in two parts: trajectory curve and acceleration profile. The best trajectory curve is picked from a set of candidate curves, where each curve is evaluated by solving a subproblem with the differential evolution(DE) algorithm. The more iterations DE performs, the more accurate the evaluation will become. Thus, we intelligently allocate the iterations to individual curves so as to reduce the total number of iterations performed. Meanwhile, the selected best curve is ensured to be one of the truly top curves with a high enough probability. Simulation results show that IOODE is 20% faster than OODE while maintaining the same performance in terms of solution quality. The computing budget allocation framework presented in this paper can also be used to enhance the efficiency of other candidate-curve-based planning methods.展开更多
基金Acknowledgements The first author was supported by National Natural Science Foundation of China(Grant Nos.11101257 and 11371102)the Basic Academic Discipline Program,the 11th Five Year Plan of 211 Project for Shanghai University of Finance and Economics+1 种基金supported by National Science Foundation of USA(Grant Nos.1115834and 1317330)a Research Gift Grant from Intel Corporation
文摘The necessary condition established in Part I of this paper for the global maximizers of the maximization problem max V tr（VTAV）/tr（VTBV）＋tr（VTCV）over the Stiefel manifold{V∈Rm×l ｜VTV=Il}（l〈m）,naturally leads to a self-consistent-field（SCF）iteration for computing a maximizer.In this part,we analyze the global and local convergence of the SCF iteration,and show that the necessary condition for the global maximizers is fulfilled at any convergent point of the sequences of approximations generated by the SCF iteration.This is one of the advantages of the SCF iteration over optimization-based methods.Preliminary numerical tests are reported and show that the SCF iteration is very efficient by comparing with some manifold-based optimization methods.
基金supported by the National Natural Science Foundation of China(No.61273039)
文摘In this paper, on-road trajectory planning is solved by introducing intelligent computing budget allocation(ICBA) into a candidate-curve-based planning algorithm, namely, ordinal-optimization-based differential evolution(OODE). The proposed algorithm is named IOODE with ‘I' representing ICBA. OODE plans the trajectory in two parts: trajectory curve and acceleration profile. The best trajectory curve is picked from a set of candidate curves, where each curve is evaluated by solving a subproblem with the differential evolution(DE) algorithm. The more iterations DE performs, the more accurate the evaluation will become. Thus, we intelligently allocate the iterations to individual curves so as to reduce the total number of iterations performed. Meanwhile, the selected best curve is ensured to be one of the truly top curves with a high enough probability. Simulation results show that IOODE is 20% faster than OODE while maintaining the same performance in terms of solution quality. The computing budget allocation framework presented in this paper can also be used to enhance the efficiency of other candidate-curve-based planning methods.
