共查询到20条相似文献,搜索用时 484 毫秒
1.
Recent studies on the kernel function-based primal-dual interior-point algorithms indicate that a kernel function not only represents a measure of the distance between the iteration and the central path, but also plays a critical role in improving the computational complexity of an interior-point algorithm. In this paper, we propose a new class of parameterized kernel functions for the development of primal-dual interior-point algorithms for solving linear programming problems. The properties of the proposed kernel functions and corresponding parameters are investigated. The results lead to a complexity bounds of ${O\left(\sqrt{n}\,{\rm log}\,n\,{\rm log}\,\frac{n}{\epsilon}\right)}$ for the large-update primal-dual interior point methods. To the best of our knowledge, this is the best known bound achieved. 相似文献
2.
Yan Qin BAI Guo Qiang WANG 《数学学报(英文版)》2007,23(11):2027-2042
A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and quadratic. Some new tools for the analysis of the algorithms are proposed. The complexity bounds of O(√Nlog N log N/ε) for large-update methods and O(√Nlog N/ε) for smallupdate methods match the best known complexity bounds obtained for these methods. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q. 相似文献
3.
Let θ > 1 and let ϕ : [0,1] → ℂ be such that the two-sided series
converges for all x ∊ [0,1], (then necessarily φ(0) = φ(1) = 0).Suppose
Define
For different classes of functions φ we show that
À notre ami, Jean-Louis Nicolas2000 Mathematics Subject Classification: Primary—11B83, 11B99 相似文献
4.
Behrouz Kheirfam 《Numerical Algorithms》2012,61(4):659-680
In this paper we propose primal-dual interior-point algorithms for semidefinite optimization problems based on a new kernel function with a trigonometric barrier term. We show that the iteration bounds are $O(\sqrt{n}\log(\frac{n}{\epsilon}))$ for small-update methods and $O(n^{\frac{3}{4}}\log(\frac{n}{\epsilon}))$ for large-update, respectively. The resulting bound is better than the classical kernel function. For small-update, the iteration complexity is the best known bound for such methods. 相似文献
5.
In this paper, we propose interior-point algorithms for $P_* (\kappa )$ -linear complementarity problem based on a new class of kernel functions. New search directions and proximity measures are defined based on these functions. We show that if a strictly feasible starting point is available, then the new algorithm has $\mathcal{O }\bigl ((1+2\kappa )\sqrt{n}\log n \log \frac{n\mu ^0}{\epsilon }\bigr )$ and $\mathcal{O }\bigl ((1+2\kappa )\sqrt{n} \log \frac{n\mu ^0}{\epsilon }\bigr )$ iteration complexity for large- and small-update methods, respectively. These are the best known complexity results for such methods. 相似文献
6.
On the Range of the Aluthge Transform 总被引:1,自引:0,他引:1
Let
be the algebra of all bounded linear operators on a complex separable Hilbert space
For an operator
let
be the Aluthge transform of T and we define
for all
where T = U|T| is a polar decomposition of T. In this short note, we consider an elementary property of the range
of Δ. We prove that R(Δ) is neither closed nor dense in
However R(Δ) is strongly dense if
is infinite dimensional.
An erratum to this article is available at . 相似文献
7.
Recently we investigated the family of double standard maps of the circle onto itself, given by
(mod 1). Similarly to the family of Arnold standard maps of the circle,
(mod 1), if 0 < b ≤ 1 then any such map has at most one attracting periodic orbit. The values of the parameters for which such orbit exists
are grouped into Arnold tongues. Here we study the shape of the boundaries of the tongues, especially close to their tips. It turns out that the shape is
fairly regular, mainly due to the real analyticity of the maps.
Dedicated to Vladimir Igorevich Arnold on the occasion of his 70th birthday
CMUP is supported by FCT through the POCTI and POSI programs, with Portuguese and European Community structural funds. 相似文献
9.
Ming Wang Zhang 《数学学报(英文版)》2012,28(11):2313-2328
In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular function and also the usual logarithmic function. The goal of this paper is to investigate such a kernel function and show that the algorithm has favorable complexity bound in terms of the elegant analytic properties of the kernel function. The complexity bound is shown to be $O\left( {\sqrt n \left( {\log n} \right)^2 \log \frac{n} {\varepsilon }} \right)$ . This bound is better than that by the classical primal-dual interior-point methods based on logarithmic barrier function and recent kernel functions introduced by some authors in optimization fields. Some computational results have been provided. 相似文献
10.
Alessandro Perotti 《Advances in Applied Clifford Algebras》2009,19(2):441-451
We study Fueter-biregular functions of one quaternionic variable. We consider left-regular functions in the kernel of the
Cauchy–Riemann operator
. A quaternionic function is biregular if on Ω, f is invertible and . Every continuous map p from Ω to the sphere of unit imaginary quaternions induces an almost complex structure Jp on the tangent bundle of . Let be the space of (pseudo)holomorphic maps from (Ω, Jp) to (), where Lp is the almost complex structure defined by left multiplication by p. Every element of is regular, but there exist regular functions that are not holomorphic for any p. The space of biregular functions contains the invertible elements of the spaces . By means of a criterion, based on the energy-minimizing property of holomorphic maps, that characterizes holomorphic functions
among regular functions, we show that every biregular function belongs to some space .
Received: October, 2007. Accepted: February, 2008. 相似文献
12.
Recently, Girstmair and Schoissengeier studied the asymptotic behavior of the arithmetic mean of Dedekind sums
, as N → ∞. In this paper we consider the arithmetic mean of weighted differences of Dedekind sums in the form
, where
is a continuous function with
,
runs over
, the set of Farey fractions of order Q in the unit interval [0,1] and
are consecutive elements of
. We show that the limit lim
Q→∞
A
h
(Q) exists and is independent of h. 相似文献
13.
V. F. Molchanov 《Acta Appl Math》2005,86(1-2):115-129
We define canonical representations for the hyperboloid of one sheet
and for the Lobachevsky space =G/K where G=SO0(1,n–1), H=SO0(1,n–2) and K=SO(n–1), as the restriction to G of representations associated with a cone of overgroups
and
for
and respectively. We determine explicitly the interaction of Lie operators of
with operators intertwining canonical representations and representations of G associated with a cone.Mathematics Subject Classifications (2000) 43A85, 22E46, 53D55.V. F. Molchanov: Supported by grants of the Netherlands Organization for Scientific Research (NWO): 047-008-009, the Russian Foundation for Basic Research (RFBR): 01-01-00100-a, the Minobr RF: E00-1.0-156, the NTP Univ. Rossii: ur04.01.037. 相似文献
14.
Let
be the Hecke algebra of the symmetric group
over a field K of characteristic
and
a primitive
-th root of one in K. We show that an
-module is projective if and only if its restrictions to any
-parabolic subalgebra of
is projective.
Moreover, we give a new construction of blocks of
-parabolic subalgebras, in terms of skew group algebras over local commutative
algebras.
Received: 30 June 2003 相似文献
15.
Simon M. Goberstein 《Algebra Universalis》2005,53(4):407-432
A partial automorphism of a semigroup S is any isomorphism between its subsemigroups, and the set all partial automorphisms of S with respect to composition is an inverse monoid called the partial automorphism monoid of S. Two semigroups are said to be
if their partial automorphism monoids are isomorphic. A class
of semigroups is called
if it contains every semigroup
to some semigroup from
Although the class of all inverse semigroups is not
we prove that the class of inverse semigroups, in which no maximal isolated subgroup is a direct product of an involution-free periodic group and the two-element cyclic group, is
It follows that the class of all combinatorial inverse semigroups (those with no nontrivial subgroups) is
A semigroup is called
if it is isomorphic or antiisomorphic to any semigroup that is
to it. We show that combinatorial inverse semigroups which are either shortly connected [5] or quasi-archimedean [10] are
To Ralph McKenzieReceived April 15, 2004; accepted in final form October 7, 2004. 相似文献
16.
We prove the meromorphic version of the Weil–Oka approximation theorem in a reduced Stein space X and give some characterizations of meromorphically
-convex open sets of X. As an application we prove that for every meromorphically
-convex open set D of a reduced Stein space X with no isolated points there exists a family
of holomorphic functions on X such that the normality domain
of
coincides with D. Mathematics Subject Classification (2000) 32E10, 32C15, 32E30, 32A19 相似文献
17.
Let Ω be a bounded domain in with C2-smooth boundary, , of co-dimension 1, and let be a Schr?dinger operator on Ω with potential . We seek the weakest conditions we can find on the rate of growth of the potential V close to the boundary which guarantee essential self-adjointness of H on . As a special case of an abstract condition, we add optimal logarithmic type corrections to the known condition where . More precisely, we show that if, as x approaches ,
where the brackets contain an arbitrary finite number of logarithmic terms, then H is essentially self-adjoint on . The constant 1 in front of each logarithmic term is optimal. The proof is based on a refined Agmon exponential estimate
combined with a well-known multidimensional Hardy inequality.
Submitted: November 18, 2008.; Accepted: January 19, 2009.
We wish to thank F. Gesztesy, A. Laptev, M. Loss and B. Simon for useful comments and suggestions. I.N.’s research was partly
supported by the NSF grant DMS 0701026. 相似文献
18.
Let p be a prime number.
Let G be a finite
p-group and
. Denote by
the complex conjugate of
. Assume that
. We show that the number of
distinct irreducible constituents of the product
is at least
.
Received: 17 March 2003 相似文献
19.
In this article we show that the distributional point values of a tempered distribution are characterized by their Fourier
transforms in the following way: If
and
, and
is locally integrable, then
distributionally if and only if there exists k such that
, for each a > 0, and similarly in the case when
is a general distribution. Here
means in the Cesaro sense. This result generalizes the characterization of Fourier series of distributions with a distributional
point value given in [5] by
. We also show that under some extra conditions, as if the sequence
belongs to the space
for some
and the tails satisfy the estimate
,\ as
, the asymmetric partial sums\ converge to
. We give convergence results in other cases and we also consider the convergence of the asymmetric partial integrals. We
apply these results to lacunary Fourier series of distributions. 相似文献
20.
Let k 1 and
be a system of rational functions forming a strongly linearly independent set over a finite field
. Let
be arbitrarily prescribed elements. We prove that for all sufficiently large extensions
, there is an element
of prescribed order such that
is the relative trace map from
onto
We give some applications to BCH codes, finite field arithmetic and ordered orthogonal arrays. We also solve a question of Helleseth et~al. (Hypercubic 4 and 5-designs from Double-Error-Correcting codes, Des. Codes. Cryptgr. 28(2003). pp. 265–282) completely.classification 11T30, 11G20, 05B15 相似文献