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Global solution of nonlinear mixed-integer bilevel programs 总被引:1,自引:0,他引:1
Alexander Mitsos 《Journal of Global Optimization》2010,47(4):557-582
An algorithm for the global optimization of nonlinear bilevel mixed-integer programs is presented, based on a recent proposal
for continuous bilevel programs by Mitsos et al. (J Glob Optim 42(4):475–513, 2008). The algorithm relies on a convergent
lower bound and an optional upper bound. No branching is required or performed. The lower bound is obtained by solving a mixed-integer
nonlinear program, containing the constraints of the lower-level and upper-level programs; its convergence is achieved by
also including a parametric upper bound to the optimal solution function of the lower-level program. This lower-level parametric
upper bound is based on Slater-points of the lower-level program and subsets of the upper-level host sets for which this point
remains lower-level feasible. Under suitable assumptions the KKT necessary conditions of the lower-level program can be used
to tighten the lower bounding problem. The optional upper bound to the optimal solution of the bilevel program is obtained
by solving an augmented upper-level problem for fixed upper-level variables. A convergence proof is given along with illustrative
examples. An implementation is described and applied to a test set comprising original and literature problems. The main complication
relative to the continuous case is the construction of the parametric upper bound to the lower-level optimal objective value,
in particular due to the presence of upper-level integer variables. This challenge is resolved by performing interval analysis
over the convex hull of the upper-level integer variables. 相似文献
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Liondas CA; Chrissoulidis DP 《The Quarterly Journal of Mechanics and Applied Mathematics》2007,60(3):275-287
This paper is intended to clarify a misunderstanding concerningthe source singularity of the electric Green's tensor for aperfectly conducting semi-infinite cone of circular cross-section.Tai's series expansion of the Green's tensor is known to lacka singular term at the source region. Jones has reconstructedthe solution to this problem and has pointed out the differencebetween his result and that of Tai. The aim of our paper isto demonstrate that, although Jones's closed-form solution iscorrect, there is a mistake in his comparison with Tai's seriessolution. We conclude that one of the two additional singularterms that Jones claims as missing from Tai's formula must beomitted. Besides, we compare Jones's closed-form solution withSmyshlyaev's solution to the very same problem. We concludethat the magnetic field expressions given by Jones and Smyshlyaevcoincide, but a singular term is missing from Smyshlyaev's expressionfor the electric field. 相似文献
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Goodman TNT; Micchelli CA; Rodriguez G; Seatzu S 《IMA Journal of Numerical Analysis》1998,18(3):331-354
It is shown that, under certain conditions, orthonormalizingthe positive integer shifts of an exponentially decaying functionon the half line by the Gram-Schmidt process leads to a limitingprofile given by orthonormalizing all their integer shifts onthe whole line. These results derive from properties of Choleskyfactorization of bi-infinite and semi-infinite matrices. Anexample is provided by the negative exponential function andconjectures are given, supported by numerical evidence, forthe Gaussian and Lorentz function. 相似文献
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从烟草(品种革新一号)单倍体花粉植株的叶和茎产生的愈伤组织,结合悬浮培养,获得的细胞分离出原生质体。在液体培养基中静置培养,12小时后原生质体开始变为卵圆形,细胞壁明显可见,24小时后完成第一次细胞分裂。以后继续分裂形成浅黄色的愈伤组织,在培养四星期后可达1毫米大小,再放到转床上进行旋转培养18天左右,愈伤组织可达3—4毫米大小。当转移到分化培养基后,分别分化出苗及根,长成完整的植株。 原生质体再生细胞的分裂与分化,不仅受不同器官来源的愈伤组织及其年龄的影响;还受分化培养基的基本成份及所用细胞分裂素的类型等的影响。 相似文献
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本文利用中心流面法的概念,指出叶轮机械的设计白变数在内、外环壁面上应有附加的限制条件,并导得其具体简明方程。同时,还定性地分析了S1流面的翘曲情况。 相似文献