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1.
F. Jarre 《Mathematical Programming》1990,49(1-3):341-358
This work examines the method of analytic centers of Sonnevend when applied to solve generalized convex quadratic programs — where also the constraints are given by convex quadratic functions. We establish the existence of a two-sided ellipsoidal approximation for the set of feasible points around its center and show, that a simple (zero order) algorithm starting from an initial center of the feasible set generates a sequence of strictly feasible points whose objective function values converge to the optimal value. Concerning the speed of convergence it is shown that an upper bound for the gap in between the objective function value and the optimal value is reduced by a factor of with
iterations wherem is the number of inequality constraints. Here, each iteration involves the computation of one Newton step. The bound of
Newton iterations to guarantee an error reduction by a factor of in the objective function is as good as the one currently given forlinear programs. However, the algorithm considered here is of theoretical interest only, full efficiency of the method can only be obtained when accelerating it by some (higher order) extrapolation scheme, see e.g. the work of Jarre, Sonnevend and Stoer.This work was supported by the Deutsche Forschungsgemeinschaft, Schwerpunktprogramm für anwendungsbezogene Optimierung und Steuerung. 相似文献
2.
Jianming Miao 《Mathematical Programming》1995,69(1-3):355-368
An interior-point predictor-corrector algorithm for theP
*()-matrix linear complementarity problem is proposed. The algorithm is an extension of Mizuno—Todd—Ye's predictor—corrector algorithm for linear programming problem. The extended algorithm is quadratically convergent with iteration complexity
. It is the first polynomially and quadratically convergent algorithm for a class of LCPs that are not necessarily monotone. 相似文献
3.
Andrzej Stachurski 《Mathematical Programming》1981,20(1):196-212
In this paper the so-called Broyden's bounded-class of methods is considered. It contains as a subclass Broyden's restricted-class of methods, in which the updating matrices retain symmetry and positive definiteness. These iteration methods are used for solving unconstrained minimization problems of the following form:
It is assumed that the step-size coefficient
k = 1 in each iteration and the functionalf : R
n R1 satisfies the standard assumptions, viz.f is twice continuously differentiable and the Hessian matrix is uniformly positive definite and bounded (there exist constantsm, M > 0 such that my2 y,
for ally R
n) and satisfies a Lipschitz-like condition at the optimal point
, the gradient vanishes at
Under these assumptions the local convergence of Broyden's methods is proved. Furthermore, the Q-superlinear convergence is shown. 相似文献
4.
Nous montrons que toute fonction séparément finement surharmonique sur un ouvert de la topologie produit
n_1×s×
n_k des topologies fines des espaces R
n
1,. . ., R
n
k,
n_1×s×
n_k-localement bornée inférieurement est finement surharmonique dans . On en déduit que toute fonction séparément finement harmonique,
n_1×s×
n_k-localement bornée sur est finement harmonique dans .Separately Finely Superharmonic Functions
Abstract.We prove that every separately finely surperharmonic function on an open set in R
n
1×s×R
n
k for the product
n_1×s×
n_k of the fine topologies on the spaces R
n
1,. . ., R
n
k,
n_1×s×
n-klocally lower bounded, is finely superharmonic in . We then deduce that every separateltly finely harmonic function
n_1×s×
n
k-locally bounded in is finely harmonic. 相似文献
5.
Werner-Georg Nowak 《Monatshefte für Mathematik》1979,87(4):297-307
In this paper we consider lattice points in domains bounded by algebraic curves of the formx
n+yn=Rn fulfilling the additional condition
where and are fixed positive real numbers. The number of these lattice points is estimated for largeR and it appears that for rational or badly approximable and the error term in the final result can be made smaller (at least forn3) than it is best possible when counting the lattice points without the additional condition indicated above. 相似文献
6.
Dr. John Walsh 《Probability Theory and Related Fields》1970,14(3):169-188
Summary In this paper we treat a time-symmetrical Martin boundary theory for continuous parameter Markov chains. This is done by reversing the time sense of a Markov chainX
t
in such a way as to obtain a dual Markov chain
, and considering the two chains together. Various relations between the Martin exit boundaries
and
of these processes are studied. The exit boundary
of
, is in a sense an entrance boundary forX
t
and vice versa. After a natural identification of certain points in
and
one can topologizeI
in such a way thatboth X
t and
have standard modifications in this space which are right continuous, have left limits, and are strongly Markov.Research supported in part at Stanford University, Stanford, California under AFOSR 0049. 相似文献
7.
The flag geometry =(
) of a finite projective plane of order s is the generalized hexagon of order (s, 1) obtained from by putting
equal to the set of all flags of , by putting
equal to the set of all points and lines of and where I is the natural incidence relation (inverse containment), i.e., is the dual of the double of in the sense of Van Maldeghem Mal:98. Then we say that is fully and weakly embedded in the finite projective space PG(d, q) if is a subgeometry of the natural point-line geometry associated with PG(d, q), if s = q, if the set of points of generates PG(d, q), and if the set of points of not opposite any given point of does not generate PG(d, q). Preparing the classification of all such embeddings, we construct in this paper the classical examples, prove some generalities and show that the dimension d of the projective space belongs to {6,7,8}. 相似文献
8.
István Talata 《Geometriae Dedicata》2000,80(1-3):319-329
For a d-dimensional convex body K let C(K) denote the minimum size of translational clouds for K. That is, C(K) is the minimum number of mutually non-overlapping translates of K which do not overlap K and block all the light rays emanating from any point of K. In this paper we prove the general upper bound
. Furthermore, for an arbitrary centrally symmetric d-dimensional convex body S we show
. Finally, for the d-dimensional ball Bd we obtain the bounds
. 相似文献
9.
In this article the topologically exact sequences
of locally convex spaces are characterized for which for every locally convex space F the map id : FE F Q is a homomorphism, or equivalently, the map id L : FK F E is a topological injection. This is motivated by the problem of lifting Q-valued functions with certain given properties to E-valued functions with the same or slightly weaker properties, which may also be considered as the investigation of parameter dependences of solutions of linear (differential) equations. Applications to partial differential equations and to Fredholm functions are given. 相似文献
10.
Let < SL
n
(
) be a subgroup of finite index, where n 5. Suppose acts continuously on a manifold M, where 1(M) =
n
, preserving a measure that is positive on open sets. Further assume that the induced action on H
1(M) is non-trivial. We show there exists a finite index subgroup < and a equivariant continuous map : M
n
that induces an isomorphism on fundamental group. We prove more general results providing continuous quotients in cases where 1(M) surjects onto a finitely generated torsion free nilpotent group. We also give some new examples of manifolds with actions. 相似文献
11.
We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let
denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let
and
denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of
with respect to p. By a hyper-duality of
, we mean an automorphism of
such that
for all
; and
is a duality of
.
is said to be hyper-self-dual whenever there exists a hyper-duality of
. We say that
is strongly hyper-self-dual whenever there exists a hyper-duality of
which can be expressed as conjugation by an invertible element of
. We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra. 相似文献
12.
Athanasios Kyriazis 《Aequationes Mathematicae》1984,27(1):220-230
Given a locally convex spaceE we define thelocally convex algebra of kernels
, in such a way that the set of all its proper closed 2-sided ideals coincides with the set of all closed vector subspaces of ker(h), whereh is a continuous algebra morphism of
into
b
(E). Moreover,h is a strictly irreducible representation such that every representation:
;
b
(F) (F a locally convex space) is of the form =oh, where stands for a continuous isomorphis ofIm(h) into
b
(F), for a suitable topology onIm(h). 相似文献
13.
The automorphism group of the Barnes-Wall lattice L
m in dimension 2
m
(m ; 3) is a subgroup of index 2 in a certain Clifford group
of structure 2
+
1+2m
. O
+(2m,2). This group and its complex analogue
of structure
.Sp(2m, 2) have arisen in recent years in connection with the construction of orthogonal spreads, Kerdock sets, packings in Grassmannian spaces, quantum codes, Siegel modular forms and spherical designs. In this paper we give a simpler proof of Runge@apos;s 1996 result that the space of invariants for
of degree 2k is spanned by the complete weight enumerators of the codes
, where C ranges over all binary self-dual codes of length 2k; these are a basis if m k - 1. We also give new constructions for L
m and
: let M be the
-lattice with Gram matrix
. Then L
m is the rational part of M
m, and
= Aut(Mm). Also, if C is a binary self-dual code not generated by vectors of weight 2, then
is precisely the automorphism group of the complete weight enumerator of
. There are analogues of all these results for the complex group
, with doubly-even self-dual code instead of self-dual code. 相似文献
14.
Angelo Sonnino 《Journal of Geometry》1999,66(1-2):187-191
An infinite family of largek-arcs in the inversive plane
over a finite field GF(q), withq 1 (mod 3),q71 orq {17,23, 27,29,41,47,49,53,59} is constructed.Research supported by G.N.S.A.G.A. of C.N.R., project Applicazioni della matematica per la tecnologia e la società, subproject Calcolo simbolico. 相似文献
15.
Sanming Zhou 《Czechoslovak Mathematical Journal》1998,48(1):45-53
Let G be a graph with order p, size q and component number . For each i between p – and q, let
be the family of spanning i-edge subgraphs of G with exactly components. For an integer-valued graphical invariant if H H
is an adjacent edge transformation (AET) implies |(H)-(H')|1 then is said to be continuous with respect to AET. Similarly define the continuity of with respect to simple edge transformation (SET). Let M
j() and m
j() be the invariants defined by
. It is proved that both M
p–() and m
p–(;) interpolate over
, if is continuous with respect to AET, and that M
j() and m
j() interpolate over
, if is continuous with respect to SET. In this way a lot of known interpolation results, including a theorem due to Schuster etc., are generalized. 相似文献
16.
A. M. Protopopov 《Algebra and Logic》2003,42(4):279-286
We study into the question of whether a partial order can be induced from a partially right-ordered group
onto a space
of right cosets of
w.r.t. some subgroup
of
. Examples are constructed showing that the condition of being convex for
in
is insufficient for this. A necessary and sufficient condition (in terms of a subgroup
and a positive cone
of
) is specified under which an order of
can be induced onto
. Sufficient conditions are also given. We establish properties of the class of partially right-ordered groups
for which
is partially ordered for every convex subgroup
, and properties of the class of groups such that
is partially ordered for every partial right order
on
and every subgroup
that is convex under
. 相似文献
17.
A. L. Chistov 《Journal of Mathematical Sciences》2003,113(5):689-717
Consider a projective algebraic variety V defined as the set of common zeros of a family of homogeneous polynomials of degree less than d in
variables with coefficients from a field k of zero characteristic. We prove that V can be represented as a union (respectively, a disjoint union) of at most
(respectively,
) smooth quasiprojective algebraic varieties such that the degrees of these varieties are bounded from above by
, where
depends only on n. We propose algorithms for constructing regular sequences and sequences of local parameters for irreducible components of V and for computing the dimension of a real variety. The complexity of these algorithms is polynomial in the size of the input and in
. Bibliography: 15 titles. 相似文献
18.
19.
We consider the family {X
, 0} of solution to the heat equation on [0,T]×[0,1] perturbed by a small space-time white noise, that is
t
X
=
X
+b({X
})+({X
})
. Then, for a large class of Borelian subsets of the continuous functions on [0,T]×[0,1], we get an asymptotic expansion of P({X
}A) as 0. This kind of expansion has been handled for several stochastic systems, ranging from Wiener integrals to diffusion processes. 相似文献
20.
V. L. Sharan 《Journal of Mathematical Sciences》2001,107(1):3601-3603
A new criterion of solvability of the interpolation problem f(
n
)=bn in the class of functions f, analytic in the right half-plane
and such that there exists c
1(0;+) such that |f(z)|c
1exp((c1|z|)) for all z
, where is a positive increasing continuous differentiable function on [0;+), for which (t)+ as t+ and there exists c
2(0;+) such that
for all t 1 is described. 相似文献