We consider the problem about the space embedded by the space and the embedding inequality. With the HSlder inequality and interpolation inequality, we give the proof of the space embedding theorem and the space holde...We consider the problem about the space embedded by the space and the embedding inequality. With the HSlder inequality and interpolation inequality, we give the proof of the space embedding theorem and the space holder embedding theorem.展开更多
Cheng-type inequality, Cheeger-type inequality and Faber-Krahn-type inequality are generalized to Finsler manifolds. For a compact Finsler manifold with the weighted Ricci curvature bounded from below by a negative co...Cheng-type inequality, Cheeger-type inequality and Faber-Krahn-type inequality are generalized to Finsler manifolds. For a compact Finsler manifold with the weighted Ricci curvature bounded from below by a negative constant, Li-Yau's estimation of the first eigenvalue is also given.展开更多
For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a sm...For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a smooth penalty method based on a class of smooth functions. The main feature of this method is that the global solution of the penalty function is not necessarily solved at each iteration, and under mild assumptions, the method is always feasible and efficient when the evaluation of the integral function is not very expensive. The global convergence property is obtained in the absence of any constraint qualifications, that is, any accumulation point of the sequence generated by the algorithm is the solution of the SIP. Moreover, the authors show a perturbation theorem of the method and obtain several interesting results. Furthermore, the authors show that all iterative points remain feasible after a finite number of iterations under the Mangasarian-Fromovitz constraint qualification. Finally, numerical results are given.展开更多
基金Supported by Soft Science Project of Henan Province(072102210020)
文摘We consider the problem about the space embedded by the space and the embedding inequality. With the HSlder inequality and interpolation inequality, we give the proof of the space embedding theorem and the space holder embedding theorem.
基金supported by the National Natural Science Foundation of China(Nos.11471246,11171253)the Natural Science Foundation of the Anhui Higher Education Institutions(No.KJ2014A257)
文摘Cheng-type inequality, Cheeger-type inequality and Faber-Krahn-type inequality are generalized to Finsler manifolds. For a compact Finsler manifold with the weighted Ricci curvature bounded from below by a negative constant, Li-Yau's estimation of the first eigenvalue is also given.
基金supported by the National Natural Science Foundation of China under Grant Nos.10971118, 10701047 and 10901096the Natural Science Foundation of Shandong Province under Grant Nos. ZR2009AL019 and BS2010SF010
文摘For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a smooth penalty method based on a class of smooth functions. The main feature of this method is that the global solution of the penalty function is not necessarily solved at each iteration, and under mild assumptions, the method is always feasible and efficient when the evaluation of the integral function is not very expensive. The global convergence property is obtained in the absence of any constraint qualifications, that is, any accumulation point of the sequence generated by the algorithm is the solution of the SIP. Moreover, the authors show a perturbation theorem of the method and obtain several interesting results. Furthermore, the authors show that all iterative points remain feasible after a finite number of iterations under the Mangasarian-Fromovitz constraint qualification. Finally, numerical results are given.
