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1.
To minimize a convex function, we combine Moreau-Yosida regularizations, quasi-Newton matrices and bundling mechanisms. First
we develop conceptual forms using “reversal” quasi-Newton formulae and we state their global and local convergence. Then,
to produce implementable versions, we incorporate a bundle strategy together with a “curve-search”. No convergence results
are given for the implementable versions; however some numerical illustrations show their good behaviour even for large-scale
problems. 相似文献
2.
Vector and Hermite subdivision schemes both act on vector data, but since the latter one interprets the vectors as function
values and consecutive derivatives they differ by the “renormalization” of the Hermite scheme in any step. In this paper we
give an algebraic factorization method in one and several variables to relate any Hermite subdivision scheme that satisfies
the so–called spectral condition to a vector subdivision scheme. These factorizations are natural extensions of the “zero
at π” condition known for the masks of refinable functions. Moreover, we show how this factorization can be used to investigate
different forms of convergence of the Hermite scheme and why the multivariate situation is conceptionally more intricate than
the univariate one. Finally, we give some examples of such factorizations. 相似文献
3.
Kalpana Dahiya Surjeet Kaur Suneja Vanita Verma 《Computational Optimization and Applications》2007,36(1):67-82
In this paper a minimization problem with convex objective function subject to a separable convex inequality constraint “≤”
and bounded variables (box constraints) is considered. We propose an iterative algorithm for solving this problem based on
line search and convergence of this algorithm is proved. At each iteration, a separable convex programming problem with the
same constraint set is solved using Karush-Kuhn-Tucker conditions. Convex minimization problems subject to linear equality/
linear inequality “≥” constraint and bounds on the variables are also considered. Numerical illustration is included in support
of theory. 相似文献
4.
We have constructed an algorithm for the asymptotic approximation of the solutions of inverse singularly perturbed boundary-value
problems of the convection-diffusion type with unknown diffusion coefficient, depending on the coordinates of a quadrangular
curvilinear domain of filtration. The case of sufficient smoothness and consistency of the overdetermination, initial, and
boundary conditions is considered. Unlike the construction of an algorithm for the solution of similar problems in doubly
connected domains, here, in the corresponding relations, there appear corrections taking into account the influence of “lateral
sources of pollution.” With the help of this algorithm, we have carried out a computer experiment, the results of which confirm
the well-known fact of “strong sensitivity” of the model to assignment of the overdetermination condition. In particular,
we have revealed the specific character of influence of this condition on the required diffusion coefficient depending on
the filtration velocity. 相似文献
5.
We prove strong convergence of the viscosity approximation process for nonexpansive nonself multimaps. Furthermore, an explicit iteration process which converges strongly to a fixed point of multimap T is constructed. It is worth mentioning that, unlike other authors, we do not impose the condition "Tz = {z}" on the map T. 相似文献
6.
Luka Grubišić 《Integral Equations and Operator Theory》2009,65(1):51-81
We prove optimal convergence estimates for eigenvalues and eigenvectors of a class of singular/stiff perturbed problems. Our
profs are constructive in nature and use (elementary) techniques which are of current interest in computational Linear Algebra
to obtain estimates even for eigenvalues which are in gaps of the essential spectrum. Further, we also identify a class of
“regular” stiff perturbations with (provably) good asymptotic properties. The Arch Model from the theory of elasticity is
presented as a prototype for this class of perturbations. We also show that we are able to study model problems which do not
satisfy this regularity assumption by presenting a study of a Schroedinger operator with singular obstacle potential. 相似文献
7.
Walter J. Gutjahr 《Central European Journal of Operations Research》2006,14(1):59-86
The paper investigates a stochastic model where two agents (persons, companies, institutions, states, software agents or other)
learn interactive behavior in a series of alternating moves. Each agent is assumed to perform “stimulus-response-consequence”
learning, as studied in psychology. In the presented model, the response of one agent to the other agent's move is both the
stimulus for the other agent's next move and part of the consequence for the other agent's previous move. After deriving general
properties of the model, especially concerning convergence to limit cycles, we concentrate on an asymptotic case where the
learning rate tends to zero (“slow learning”). In this case, the dynamics can be described by a system of deterministic differential
equations. For reward structures derived from [2×2] bimatrix games, fixed points are determined, and for the special case
of the prisoner's dilemma, the dynamics is analyzed in more detail on the assumptions that both agents start with the same
or with different reaction probabilities. 相似文献
8.
A new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual
problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual” to the Dinkelbach-type
algorithm for generalized fractional programs since it approximates the optimal objective value of the dual (primal) problem
from below. Convergence results for this algorithm are derived and an easy condition to achieve superlinear convergence is
also established. Moreover, under some additional assumptions the algorithm also recovers at the same time an optimal solution
of the primal problem. We also consider a variant of this new algorithm, based on scaling the “dual” parametric function.
The numerical results, in case of quadratic-linear ratios and linear constraints, show that the performance of the new algorithm
and its scaled version is superior to that of the Dinkelbach-type algorithms. From the computational results it also appears
that contrary to the primal approach, the “dual” approach is less influenced by scaling.
This research was carried out at the Econometric Institute, Erasmus University, Rotterdam, the Netherlands and was supported
by J.N.I.C.T. (Portugal) under contract BD/707/90-RM. 相似文献
9.
In this work, we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the
dynamics of a population in which individuals have two distinct life-stages: an “active” phase when individuals grow, reproduce
and die and a second “resting” phase when individuals only grow. Transition between these two phases depends on individuals’
size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state
space. Then, we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions
of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous
exponential growth. 相似文献
10.
Gergő Nemes 《Archiv der Mathematik》2010,95(2):161-169
Using a series transformation, the Stirling-De Moivre asymptotic series approximation to the Gamma function is converted into
a new one with better convergence properties. The new formula is being compared with those of Stirling, Laplace, and Ramanujan
for real arguments greater than 0.5 and turns out to be, for equal number of “correction” terms, numerically superior to all
of them. As a side benefit, a closed-form approximation has turned up during the analysis which is about as good as 3rd order
Stirling’s (maximum relative error smaller than 1e − 10 for real arguments greater or equal to 24). 相似文献
11.
Summary The formal asymptotic analysis of Latifi et al. [4] suggests that the Mixmaster Universe model possesses movable transcendental
singularities and thus is nonintegrable in the sense that it does not satisfy the Painlevé property (i.e., singularities with
nonalgebraic branching). In this paper, we present numerical evidence of the nonintegrability of the Mixmaster model by studying
the singularity patterns in the complext-plane, wheret is the “physical” time, as well as in the complex τ-plane, where τ is the associated “logarithmic” time. More specifically,
we show that in the τ-plane there appears to exist a “natural boundary” of remarkably intricate structure. This boundary lies
at the ends of a sequence of smaller and smaller “chimneys” and consists of the type of singularities studied in [4], on which
pole-like singularities accumulate densely. We also show numerically that in the complext-plane there appear to exist complicated, dense singularity patterns and infinitely-sheeted solutions with sensitive dependence
on initial conditions. 相似文献
12.
S. A. Nazarov 《Journal of Mathematical Sciences》1996,80(5):1989-2034
The asymptotic series for solutions of the mixed boundary-value problem for the Poisson equation in a domain, which is a junction
of singularly degenerating domains, are constructed. In this paper, which is the first part of the publication, the three-dimensional
problem (“wheel hub with spokes”) and the analogous two-dimensional problems are considered. The methods of matched and compound
asymptotic expansions are used. It is shown that a special self-adjoint extension of the operator of the limit problem in
the “hub” supplied by the straight-line segments (“limits of spokes”) can be chosen as an asymptotical model of the problem
in question; the extension parameters are to be some integral characteristics of the boundary-layer problems. Bibliography:
39 titles.
Translated from Trudy Seminara imeni I. G. Petrovskogo. No. 18, pp. 3–78, 1995. 相似文献
13.
In statistics of extremes, inference is often based on the excesses over a high random threshold. Those excesses are approximately
distributed as the set of order statistics associated to a sample from a generalized Pareto model. We then get the so-called
“maximum likelihood” estimators of the tail index γ. In this paper, we are interested in the derivation of the asymptotic distributional properties of a similar “maximum likelihood”
estimator of a positive tail index γ, based also on the excesses over a high random threshold, but with a trial of accommodation of bias in the Pareto model underlying
those excesses. We next proceed to an asymptotic comparison of the two estimators at their optimal levels. An illustration
of the finite sample behaviour of the estimators is provided through a small-scale Monte Carlo simulation study.
Research partially supported by FCT/POCTI and POCI/FEDER. 相似文献
14.
David German 《Mathematics and Financial Economics》2011,4(4):287-297
We study a financial model with a non-trivial price impact effect. In this model we consider the interaction of a large investor
trading in an illiquid security, and a market maker who is quoting prices for this security. We assume that the market maker
quotes the prices such that by taking the other side of the investor’s demand, the market maker will arrive at maturity with
the maximal expected utility of the terminal wealth. Within this model we provide an explicit recursive pricing formula for
an exponential utility function, as well as an asymptotic expansion for the price for a “small” simple demand. 相似文献
15.
A thorough convergence analysis of the Control Reduced Interior Point Method in function space is performed. This recently
proposed method is a primal interior point pathfollowing scheme with the special feature that the control variable is eliminated
from the optimality system. Apart from global linear convergence we show that this method converges locally superlinearly,
if the optimal solution satisfies a certain non-degeneracy condition. In numerical experiments we observe that a prototype
implementation of our method behaves as predicted by our theoretical results.
Supported by the DFG Research Center Matheon “Mathematics for key technologies”. 相似文献
16.
We study the model M consisting of “general games” with noncompact action space, together with an associated abstract rationality function. We
prove that M is structurally stable and robust to ϵ-equilibria for “almost all” parameters. As applications, we investigate structural
stability and robustness to bounded rationality for noncooperative games, multiobjective optimizations and fixed point problems
satisfying existence and some continuity conditions. Specifically, we introduce concrete rationality functions for such three
kinds of problems with both payoffs and strategy sets, objective functions and domain spaces, and correspondence and domain
spaces as parameters, respectively, and show the generic structural stability and robustness to bounded rationality for the
corresponding model Ms. 相似文献
17.
In this paper we deal with the iterative computation of negative curvature directions of an objective function, within large
scale optimization frameworks. In particular, suitable directions of negative curvature of the objective function represent
an essential tool, to guarantee convergence to second order critical points. However, an “adequate” negative curvature direction
is often required to have a good resemblance to an eigenvector corresponding to the smallest eigenvalue of the Hessian matrix.
Thus, its computation may be a very difficult task on large scale problems. Several strategies proposed in literature compute
such a direction relying on matrix factorizations, so that they may be inefficient or even impracticable in a large scale
setting. On the other hand, the iterative methods proposed either need to store a large matrix, or they need to rerun the
recurrence.
On this guideline, in this paper we propose the use of an iterative method, based on a planar Conjugate Gradient scheme. Under
mild assumptions, we provide theory for using the latter method to compute adequate negative curvature directions, within
optimization frameworks. In our proposal any matrix storage is avoided, along with any additional rerun. 相似文献
18.
The score tests of independence in multivariate extreme values derived by Tawn (Tawn, J.A., “Bivariate extreme value theory:
models and estimation,” Biometrika 75, 397–415, 1988) and Ledford and Tawn (Ledford, A.W. and Tawn, J.A., “Statistics for near independence in multivariate
extreme values,” Biometrika 83, 169–187, 1996) have non-regular properties that arise due to violations of the usual regularity conditions of maximum
likelihood. Two distinct types of regularity violation are encountered in each of their likelihood frameworks: independence
within the underlying model corresponding to a boundary point of the parameter space and the score function having an infinite
second moment. For applications, the second form of regularity violation has the more important consequences, as it results
in score statistics with non-standard normalisation and poor rates of convergence. The corresponding tests are difficult to
use in practical situations because their asymptotic properties are unrepresentative of their behaviour for the sample sizes
typical of applications, and extensive simulations may be needed in order to evaluate adequately their null distribution.
Overcoming this difficulty is the primary focus of this paper.
We propose a modification to the likelihood based approaches used by Tawn (Tawn, J.A., “Bivariate extreme value theory: models
and estimation,” Biometrika 75, 397–415, 1988) and Ledford and Tawn (Ledford, A.W. and Tawn, J.A., “Statistics for near independence in multivariate
extreme values,” Biometrika 83, 169–187, 1996) that provides asymptotically normal score tests of independence with regular normalisation and rapid convergence.
The resulting tests are straightforward to implement and are beneficial in practical situations with realistic amounts of
data.
AMS 2000 Subject Classification Primary—60G70
Secondary—62H15 相似文献
19.
Francisco J. González-Castaño Enrique Costa-Montenegro Juan C. Burguillo-Rial Ubaldo García-Palomares 《Computational Optimization and Applications》2008,40(3):405-419
In this paper, we study the application of non-monotone derivative-free optimization algorithms to wireless local area networks
(WLAN) planning, which can be modeled as an unconstrained minimization problem. We wish to determine the access point (AP)
positions that maximize coverage in order to provide connectivity to static and mobile users. As the objective function of
the optimization model is not everywhere differentiable, previous research has discarded gradient methods and employed heuristics
such as neighborhood search (NS) and simulated annealing (SA). In this paper, we show that the model fulfills the conditions
required by recently proposed non-monotone derivative-free (DF) algorithms. Unlike SA, DF has guaranteed convergence. The
numerical tests reveal that a tailored DF implementation (termed “zone search”) outperforms NS and SA.
A collaboration between U. of Vigo, Spain and USB, Venezuela. 相似文献
20.
Christof Külske 《Probability Theory and Related Fields》2001,119(1):1-30
Can the joint measures of quenched disordered lattice spin models (with finite range) on the product of spin-space and disorder-space
be represented as (suitably generalized) Gibbs measures of an “annealed system”? - We prove that there is always a potential
(depending on both spin and disorder variables) that converges absolutely on a set of full measure w.r.t. the joint measure
(“weak Gibbsianness”). This “positive” result is surprising when contrasted with the results of a previous paper [K6], where
we investigated the measure of the set of discontinuity points of the conditional expectations (investigation of “a.s. Gibbsianness”).
In particular we gave natural “negative” examples where this set is even of measure one (including the random field Ising
model). Further we discuss conditions giving the convergence of vacuum potentials and conditions for the decay of the joint
potential in terms of the decay of the disorder average over certain quenched correlations. We apply them to various examples.
From this one typically expects the existence of a potential that decays superpolynomially outside a set of measure zero.
Our proof uses a martingale argument that allows to cut (an infinite-volume analogue of) the quenched free energy into local
pieces, along with generalizations of Kozlov's constructions.
Received: 11 November 1999 / Revised version: 18 April 2000 / Published online: 22 November 2000
RID="*"
ID="*" Work supported by the DFG Schwerpunkt `Wechselwirkende stochastische Systeme hoher Komplexit?t' 相似文献