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851.
The main goals of this paper are to: i) relate two iteration-complexity bounds derived for the Mizuno-Todd-Ye predictor-corrector
(MTY P-C) algorithm for linear programming (LP), and; ii) study the geometrical structure of the LP central path. The first
iteration-complexity bound for the MTY P-C algorithm considered in this paper is expressed in terms of the integral of a certain
curvature function over the traversed portion of the central path. The second iteration-complexity bound, derived recently
by the authors using the notion of crossover events introduced by Vavasis and Ye, is expressed in terms of a scale-invariant
condition number associated with m × n constraint matrix of the LP. In this paper, we establish a relationship between these bounds by showing that the first one
can be majorized by the second one. We also establish a geometric result about the central path which gives a rigorous justification
based on the curvature of the central path of a claim made by Vavasis and Ye, in view of the behavior of their layered least
squares path following LP method, that the central path consists of long but straight continuous parts while the remaining curved part is relatively “short”.
R. D. C. Monteiro was supported in part by NSF Grants CCR-0203113 and CCF-0430644 and ONR grant N00014-05-1-0183. T. Tsuchiya
was supported in part by Japan-US Joint Research Projects of Japan Society for the Promotion of Science “Algorithms for linear
programs over symmetric cones” and the Grants-in-Aid for Scientific Research (C) 15510144 of Japan Society for the Promotion
of Science. 相似文献
852.
Let G be a digraph (without parallel edges) such that every directed cycle has length at least four; let β(G) denote the size of the smallest subset X ? E(G) such that G?X has no directed cycles, and let γ(G) be the number of unordered pairs {u, v} of vertices such that u, v are nonadjacent in G. It is easy to see that if γ(G) = 0 then β(G) = 0; what can we say about β(G) if γ(G) is bounded?
We prove that in general β(G) ≤ γ(G). We conjecture that in fact β(G) ≤ ½γ(G) (this would be best possible if true), and prove this conjecture in two special cases:
相似文献
- when V(G) is the union of two cliques
- when the vertices of G can be arranged in a circle such that if distinct u, v, w are in clockwise order and uw is a (directed) edge, then so are both uv, vw.
853.
Imre Patyi 《Mathematische Annalen》2008,341(2):455-482
Let X be a Banach space with a countable unconditional basis (e.g., X = ℓ
2 Hilbert space), Ω ⊂ X pseudoconvex open, E → Ω a locally trivial holomorphic vector bundle with a Banach space Z for fiber type, the sheaf of germs of holomorphic sections of E → Ω, and Z
1 the Banach space . Then and Ω × Z
1 are holomorphically isomorphic, is acyclic and E is so to speak stably trivial over Ω in a generalized sense. We also show that if E is continuously trivial over Ω, then E is holomorphically trivial over Ω. In particular, if Z = ℓ
2 or Ω is contractible, then E is holomorphically trivial over Ω. Some applications are also given.
To my dear little daughter, Sári Mangala, on her third birthday.
Supported in part by a Research Initiation Grant from Georgia State University. 相似文献
854.
Milutin Dostanić 《Journal d'Analyse Mathématique》2008,104(1):13-23
It is shown that the Berezin transform B on L
p
(D), where D is the unit disc, has norm
. Furthermore, the norms of a family of operators (on L
p
(D)) whose kernels are moduli of Bergman type kernels are also calculated.
Partially supported by MNZZS, Grant
ON144010 相似文献
855.
This paper gives lower estimates for the frequency modules of almost periodic solutions to equations of the form
, where A generates a strongly continuous semigroup in a Banach space
, F(t,x) is 2π-periodic in t and continuous in (t,x), and f is almost periodic. We show that the frequency module ℳ(u) of any almost periodic mild solution u of (*) and the frequency module ℳ(f) of f satisfy the estimate e
2π
iℳ(f)⊂e
2π
iℳ(u). If F is independent of t, then the estimate can be improved: ℳ(f)⊂ℳ(u). Applications to the nonexistence of quasi-periodic solutions are also given. 相似文献
856.
Sadek Gala 《Applications of Mathematics》2008,53(6):561-582
Consider the Navier-Stokes equation with the initial data a ∈ L
σ
2(ℝ
d
). Let u and v be two weak solutions with the same initial value a. If u satisfies the usual energy inequality and if ∇v ∈ L
2((0, T); (ℝ
d
)
d
) where (ℝ
d
) is the multiplier space, then we have u = v. 相似文献
857.
We classify the real hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians SU2,m/S(U2⋅Um), m?2. Each can be described as a tube over a totally geodesic SU2,m−1/S(U2⋅Um−1) in SU2,m/S(U2⋅Um) or a horosphere whose center at infinity is singular. 相似文献
858.
859.
Since the decline of the Cold War, the risk of major conflict between powerful, industrialized nations has decreased. Insecurities in the 21st century are more apt to arise from the debris of imploding states. Such situations may require intervention—military or otherwise—by concerned states. To meet this new operational challenge, nations must adapt their planning procedures to account for Security, Stabilization, Transition, and Reconstruction Operations (SSTRO). This paper develops a project scheduling framework for post-conflict reconstruction that schedules reconstruction activities to maximize the positive impact to the local economy during the initial phase of SSTRO. Specifically, this paper builds on the Multimode Resource Constrained Project Scheduling Problem with Generalized Precedence Relations (MM-RCPSP-GPR) using goal programming to maximize the reconstruction operations’ positive impact to local population's economic welfare. This MM-RCPSP-GPR variant is applied to a notional example to illustrate its potential use in post-conflict SSTRO. The basic framework can be extended to other settings. 相似文献
860.
Xiaopeng Zhao Min Zhang Changchun Liu 《Mathematical Methods in the Applied Sciences》2013,36(2):169-181
This paper is concerned with a fourth‐order parabolic equation in one spatial dimension. On the basis of Leray–Schauder's fixed point theorem, we prove the existence and uniqueness of global weak solutions. Moreover, we also consider the regularity of solution and the existence of global attractor. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献