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101.
《Optimization》2012,61(3):301-316
We consider equilibrium problems in the framework of the formulation proposed by Blum and Oettli, which includes variational inequalities, Nash equilibria in noncooperative games, and vector optimization problems, for instance, as particular cases. We show that such problems are particular instances of convex feasibility problems with infinitely many convex sets, but with additional structure, so that projection algorithms for convex feasibility can be modified in order to improve their convergence properties, mainly achieving global convergence without either compactness or coercivity assumptions. We present a sequential projections algorithm with an approximately most violated constraint control strategy, and two variants where exact orthogonal projections are replaced by approximate ones, using separating hyperplanes generated by subgradients. We include full convergence analysis of these algorithms. 相似文献
102.
《Optimization》2012,61(4-5):441-458
We consider the Hamiltonian cycle problem (HCP) embedded in a singularly perturbed Markov decision process (MDP). More specifically, we consider the HCP as an optimization problem over the space of long-run state-action frequencies induced by the MDP's stationary policies. We also consider two quadratic functionals over the same space. We show that when the perturbation parameter, ? is sufficiently small the Hamiltonian cycles of the given directed graph are precisely the maximizers of one of these quadratic functionals over the frequency space intersected with an appropriate (single) contour of the second quadratic functional. In particular, all these maximizers have a known Euclidean distance of z m (?) from the origin. Geometrically, this means that Hamiltonian cycles, if any, are the points in the frequency polytope where the circle of radius z m (?) intersects a certain ellipsoid. 相似文献
103.
A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier series. Equivalent conditions
are derived for the uniform and L
1-norm convergence of the θ-means σ
n
θ
f to the function f. If f is in a homogeneous Banach space, then the preceeding convergence holds in the norm of the space. In case θ is an element
of Feichtinger’s Segal algebra
, then these convergence results hold. Some new sufficient conditions are given for θ to be in
. A long list of concrete special cases of the θ-summation is listed. The same results are also provided in the context of
Fourier transforms, indicating how proofs have to be changed in this case.
This research was supported by Lise Meitner fellowship No M733-N04 and the Hungarian Scientific Research Funds (OTKA) No T043769,
T047128, T047132. 相似文献
104.
Hany M. El-Hosseiny 《Potential Analysis》2006,25(2):131-145
We prove general boundary limit theorems of abelian type for quotients of functions defined in the half space . The functions considered are defined as convolutions of a kernel with Borel measures defined on the boundary . Our theorems are of the form
where the approach to the limit in question is either non-tangential (Theorems 3.4 and 3.3), or radial (Theorem 3.2). The key feature is the relation of subordination in the sense of Bochner between the two kernels and . Our results generalize many known ones, such as the abelian theorem of Doob and that of Armitage for relative harmonic functions, and the results of Watson and Doob for Parabolic functions. 相似文献
105.
We prove that there exist (n − 1)-dimensional compact embedded rotational hypersurfaces with constant scalar curvature (n − 1)(n − 2)S (S > 1) of S
n
other than product of spheres for 4 ≤ n ≤ 6. As a result, we prove that Leite’s Assertion was incorrect.The project is supported by the grant No. 10531090 of NSFC. 相似文献
106.
Fatiha Alabau-Boussouira 《Journal of Evolution Equations》2006,6(1):95-112
This work is concerned with obtention of energy decay estimates for Petrowsky equation with a nonlinear dissipation which
is active only in an interior subset of the domain. We prove that the piecewise multiplier method as introduced by [20] and
[22] for the wave equation can be extended to the Petrowsky equation. Moreover, we also apply some recent results by the author
to obtain precise decay rate estimates for the energy, without specifying the growth of the nonlinear dissipation close to
the origin by means of convex properties and nonlinear integral inequalities for the energy of the solutions. 相似文献
107.
Young Jin Suh 《Monatshefte für Mathematik》2006,147(4):337-355
In this paper we give a characterization of real hypersurfaces of type B, that is, a tube over a totally real totally geodesic
in complex two-plane Grassmannians
with the shape operator A satisfying Aφ + φA = kφ, k is non-zero constant, for the structure tensor φ. 相似文献
108.
Let X be a locally compact Hausdorff space and C
0(X) the Banach space of continuous functions on X vanishing at infinity. In this paper, we shall study unbounded disjointness preserving linear functionals on C
0(X). They arise from prime ideals of C
0(X), and we translate it into the cozero set ideal setting. In particular, every unbounded disjointness preserving linear functional of c
0 can be constructed explicitly through an ultrafilter on complementary to a cozero set ideal. This ultrafilter method can be extended to produce many, but in general not all, such functionals on C
0(X) for arbitrary X. We also make some remarks where C
0(X) is replaced by a non-commutative C*-algebra. 相似文献
109.
On a Definitizable Analog of the Trigonometric Moment Problem Generating an Indefinite Toeplitz Form
We prove the existence of an integro-polynomial representation for a sequence of numbers such that there exists a difference operator mapping this sequence to a sequence that generates the solvable trigonometric moment problem. A similar result related to the power moment problem was given in [12]. 相似文献
110.
John W. Snow 《Algebra Universalis》2005,54(1):65-71
A congruence lattice L of an algebra A is called power-hereditary if every 0-1 sublattice of Ln is the congruence lattice of an algebra on An for all positive integers n. Let A and B be finite algebras. We prove
Received November 11, 2004; accepted in final form November 23, 2004. 相似文献
• | If ConA is distributive, then every subdirect product of ConA and ConB is a congruence lattice on A × B. |
• | If ConA is distributive and ConB is power-hereditary, then (ConA) × (ConB) is powerhereditary. |
• | If ConA ≅ N5 and ConB is modular, then every subdirect product of ConA and ConB is a congruence lattice. |
• | Every congruence lattice representation of N5 is power-hereditary. |