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On the Kahler-Ricci Flow on Projective Manifolds of General Type 被引量:5
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作者 Gang TIAN Zhou ZHANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2006年第2期179-192,共14页
This note concerns the global existence and convergence of the solution for Kahler-Ricci flow equation when the canonical class, Kx, is numerically effective and big. We clarify some known results regarding this flow ... This note concerns the global existence and convergence of the solution for Kahler-Ricci flow equation when the canonical class, Kx, is numerically effective and big. We clarify some known results regarding this flow on projective manifolds of general type and also show some new observations and refined results. 展开更多
关键词 Geometric evolution equations Minimal model program
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A PENALTY FUNCTION METHOD FOR SOLVING ILL-POSED BILEVEL PROGRAMMING PROBLEM VIA WEIGHTED SUMMATION 被引量:2
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作者 JIA Shihui WAN Zhongping 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2013年第6期1019-1027,共9页
For ill-posed bilevel programming problem,the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model's satisfacto... For ill-posed bilevel programming problem,the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model's satisfactory degree in application.To acquire a more satisfying solution than the optimistic one to realize the two levels' most profits,this paper considers both levels' satisfactory degree and constructs a minimization problem of the two objective functions by weighted summation.Then,using the duality gap of the lower level as the penalty function,the authors transfer these two levels problem to a single one and propose a corresponding algorithm.Finally,the authors give an example to show a more satisfying solution than the optimistic solution can be achieved by this algorithm. 展开更多
关键词 Bilevel programming duality gap penalty function satisfactory degree weighted sum-mation.
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