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51.
This paper discusses the relationship between Karmarkar's new method for linear programming and the traditional simplex method.
It is shown how null-space Karmarkar projections can be done using a basis matrix to compute the projections in the null space.
Preliminary computational evidence shows that problems exist in the choice of a basis matrix, but that, given a basis, very
inexact and computationally efficient projections are computationally sound. 相似文献
52.
J. -P. Penot 《Journal of Optimization Theory and Applications》1996,90(3):535-554
Two ways of defining a well-conditioned minimization problem are introduced and related, with emphasis on the quantitative aspects. These concepts are used to study the behavior of the solution sets of minimization problems for functions with connected sublevel sets, generalizing results of Attouch-Wets in the convex case. Applications to continuity properties of subdifferentials and to projection mappings are pointed out.We are grateful to M. Valadier for pointing out, during a lecture by the author in Montpellier in October 1990 presenting the main results of the present paper, that existence results in Section 2 of the present paper can be dissociated from estimates. 相似文献
53.
A relaxed version of Karmarkar's method is developed. This method is proved to have the same polynomial time complexity as Karmarkar's method and its efficient implementation using inexact projections is discussed. Computational results obtained using a preliminary implementation of the method are presented which indicate that the method is practicable.This research was supported in part by NSF Grants CDR 84-21402 and DMS-85-12277 and ONR Contract N00014-87-K-0214. 相似文献
54.
R.H. Marty 《Topology and its Applications》1982,14(3):305-311
Let X denote the product of m-many second countable Hausdorff spaces. Main theorems: (1) If S?X is invariant under compositions, m is weakly accessible (resp., nonmeasurable), and F?S is sequentially closed and a sequential Gσ-set which is invariant under projections for finite sets (resp., F?S is sequentially open and sequentially closed), then F is closed. (2) If S?X is invariant under projections and m is nonmeasurable, then every sequentially continuous {0, 1} valued function on S is continuous. (3) A sequentially continuous {0, 1}-valued function on an m-adic space of nonmeasurable weight is continuous. Now let X denote the product of arbitrarily many W-spaces and S?X be invariant under compositions. (4) Then in S, the closure of any Q-open subset coincides with its sequential closure. 相似文献
55.
J.C. Mason 《Numerical Algorithms》2005,38(1):61-78
By considering four kinds of Chebyshev polynomials, an extended set of (real) results are given for Chebyshev polynomial minimality in suitably weighted Hölder norms on [–1,1], as well as (L
) minimax properties, and best L
1 sufficiency requirements based on Chebyshev interpolation. Finally we establish best L
p
, L
and L
1 approximation by partial sums of lacunary Chebyshev series of the form
i=0
a
i
b
i(x) where
n
(x) is a Chebyshev polynomial and b is an odd integer 3. A complete set of proofs is provided. 相似文献
56.
Vladimir Manuilov Sergei Silvestrov 《Proceedings of the American Mathematical Society》2006,134(9):2593-2598
For a class of unbounded operators, a deformation of a Bott projection is used to construct an integer-valued invariant measuring deviation of the non-commutative deformations from the commutative originals, and its interpretation in terms of -theory of -algebras is given. Calculation of this invariant for specific important classes of unbounded operators is also presented.
57.
J. Antezana G. Corach M. Ruiz D. Stojanoff 《Proceedings of the American Mathematical Society》2006,134(4):1031-1037
We characterize those frames on a Hilbert space which can be represented as the image of an orthonormal basis by an oblique projection defined on an extension of . We show that all frames with infinite excess and frame bounds are of this type. This gives a generalization of a result of Han and Larson which only holds for normalized tight frames.
58.
Michael Röckner Weina Wu Yingchao Xie 《Stochastic Processes and their Applications》2018,128(6):2131-2151
We prove the existence and uniqueness of probabilistically strong solutions to stochastic porous media equations driven by time-dependent multiplicative noise on a general measure space , and the Laplacian replaced by a negative definite self-adjoint operator . In the case of Lipschitz nonlinearities , we in particular generalize previous results for open and Laplacian to fractional Laplacians. We also generalize known results on general measure spaces, where we succeeded in dropping the transience assumption on , in extending the set of allowed initial data and in avoiding the restriction to superlinear behavior of at infinity for -initial data. 相似文献
59.
Banach空间中α-序压缩映射的不动点定理 总被引:2,自引:0,他引:2
在Banach空间中引入了几种压缩映射,证明了一类非线性映射的不动点的存在性,并改进和推广了相应定理. 相似文献
60.
Suppose K is a closed convex nonexpansive retract of a real uniformly smooth Banach space E with P as the nonexpansive retraction. Suppose T : K → E is an asymptotically d-weakly contractive map with sequence {kn }, kn ≥ 1, lim kn = 1 and with F(T) n int (K) ≠ ø F(T):= {x ∈ K: Tx = x}. Suppose {x n } is iteratively defined by x n+1 = P((l ? knαn )x n +k n α n T(PT) n?l xn ), n = 1,2,...,x 1 ∈ K, where αn∈ (0,l) satisfies lim αn = 0 and Σαn = ∞. It is proved that {x n } converges strongly to some x * ∈ F(T)∩ int K. Furthermore, if K is a closed convex subset of an arbitrary real Banach space and T is, in addition uniformly continuous, with F(T) ≠ ø, it is proved that {xn } converges strongly to some x * ∈ F(T). 相似文献