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1.
In this paper we discuss the problem of verifying and computing optimal controls of systems whose dynamics is governed by
differential systems with a discontinuous right-hand side. In our work, we are motivated by optimal control of mechanical
systems with Coulomb friction, which exhibit such a right-hand side. Notwithstanding the impressive development of nonsmooth
and set-valued analysis, these systems have not been closely studied either computationally or analytically. We show that
even when the solution crosses and does not stay on the discontinuity, differentiating the results of a simulation gives gradients
that have errors of a size independent of the stepsize. This means that the strategy of “optimize the discretization” will
usually fail for problems of this kind. We approximate the discontinuous right-hand side for the differential equations or
inclusions by a smooth right-hand side. For these smoothed approximations, we show that the resulting gradients approach the
true gradients provided that the start and end points of the trajectory do not lie on the discontinuity and that Euler’s method
is used where the step size is “sufficiently small” in comparison with the smoothing parameter. Numerical results are presented
for a crude model of car racing that involves Coulomb friction and slip showing that this approach is practical and can handle
problems of moderate complexity. 相似文献
2.
Khalid Addi Samir Adly Daniel Goeleven Hassan Saoud 《Journal of Global Optimization》2008,40(1-3):7-27
Using the recession analysis we study necessary and sufficient conditions for the existence and the stability of a finite
semi-coercive variational inequality with respect to data perturbation. Some applications of the abstract results in mechanics
and in electronic circuits involving devices like ideal diode and practical diode are discussed.
The research of S. Adly has been supported by the “Fondation EADS” and the ANR project “Guidage”. 相似文献
3.
In this paper, we propose the treatment of complex reservoir operation problems via our newly developed tool of fuzzy criterion
decision processes. This novel approach has been shown to be a more flexible and useful analysis tool especially when it is
desirable to incorporate an expert’s knowledge into the decision models. Additionally, it has been demonstrated that this
form of decision models will usually result in an optimal solution, which guarantees the highest satisfactory degree. We provide
a practical exemplification procedure for the models presented as well as an application example. 相似文献
4.
We show that uniqueness and existence for signal reconstruction from multiscale edges in the Mallat and Zhong algorithm become
possible if we restrict our signals to Paley-Wiener space, band-limit our wavelets, and irregularly sample at the wavelet
transform (absolute) maxima—the edges—while possibly including (enough) extra points at each level. We do this in a setting
that closely resembles the numerical analysis setting of Mallat and Zhong and that seems to capture something of the essence
of their (practical) reconstruction method. Our work builds on a uniqueness result for reconstructing an L2 signal from irregular sampling of its wavelet transform of Grochenig and the related work of Benedetto, Heller, Mallat, and
Zhong. We show that the rate of convergence for this reconstruction algorithm is geometric and computable in advance. Finally,
we consider the effect on the rate of convergence of not sampling enough local maxima. 相似文献
5.
In this paper, we have suggested a penalty method to modify the combinatorial optimization problem with the linear constraints
to a global optimization problem with linear constraints. It also deals with a topic of vital significance of pump operation
optimization in a water system. In this connection we have done a lot of work to formulate a model based on a simplified flow
volume balance to resolve the problem of optimal pump operation settings of switching “ON” and “OFF” with the reduced gradient
method. This global solution approach incorporates some benefits for practical application to a real system as is shown in
the case study. 相似文献
6.
This paper proposes the use of a formal grammar for the verification of mathematical formulae for a practical mathematical
OCR system. Like a C compiler detecting syntax errors in a source file, we want to have a verification mechanism to find errors
in the output of mathematical OCR. A linear monadic context-free tree grammar (LM-CFTG) is employed as a formal framework
to define “well-formed” mathematical formulae. A cubic time parsing algorithm for LM-CFTGs is presented. For the purpose of
practical evaluation, a verification system for mathematical OCR is developed, and the effectiveness of the system is demonstrated
by using the ground-truthed mathematical document database InftyCDB-1 and a misrecognition database newly constructed for
this study. 相似文献
7.
Implementing and interpreting a data envelopment analysis model to assess the efficiency of health systems in developing countries 总被引:1,自引:0,他引:1
Alexander Christine A.; Busch Gary; Stringer Karl 《IMA Journal of Management Mathematics》2003,14(1):49-63
This paper presents a data envelopment analysis model that canbe implemented by public sector management for assessing theefficiency of a health system within a developing country. Toillustrate the practical implementation and interpretation ofthe model this study compares health systems across 51 developingcountries using 199899 data. The results of the analysisgenerated empirical indicators of efficiency, and we demonstratehow these may then be used by management in order to understandthe factors associated with good performance of a health system. 相似文献
8.
Endre Boros Peter L. Hammer Toshihide Ibaraki Alexander Kogan 《Mathematical Programming》1997,79(1-3):163-190
“Logical analysis of data” (LAD) is a methodology developed since the late eighties, aimed at discovering hidden structural
information in data sets. LAD was originally developed for analyzing binary data by using the theory of partially defined
Boolean functions. An extension of LAD for the analysis of numerical data sets is achieved through the process of “binarization”
consisting in the replacement of each numerical variable by binary “indicator” variables, each showing whether the value of
the original variable is above or below a certain level. Binarization was successfully applied to the analysis of a variety
of real life data sets. This paper develops the theoretical foundations of the binarization process studying the combinatorial
optimization problems related to the minimization of the number of binary variables. To provide an algorithmic framework for
the practical solution of such problems, we construct compact linear integer programming formulations of them. We develop
polynomial time algorithms for some of these minimization problems, and prove NP-hardness of others.
The authors gratefully acknowledge the partial support by the Office of Naval Research (grants N00014-92-J1375 and N00014-92-J4083). 相似文献
9.
Koji Nuida Satoshi Fujitsu Manabu Hagiwara Takashi Kitagawa Hajime Watanabe Kazuto Ogawa Hideki Imai 《Designs, Codes and Cryptography》2009,52(3):339-362
It has been proven that the code lengths of Tardos’s collusion-secure fingerprinting codes are of theoretically minimal order
with respect to the number of adversarial users (pirates). However, the code lengths can be further reduced as some preceding
studies have revealed. In this article we improve a recent discrete variant of Tardos’s codes, and give a security proof of
our codes under an assumption weaker than the original Marking Assumption. Our analysis shows that our codes have significantly
shorter lengths than Tardos’s codes. For example, when c = 8, our code length is about 4.94% of Tardos’s code in a practical setting and about 4.62% in a certain limit case. Our
code lengths for large c are asymptotically about 5.35% of Tardos’s codes.
A part of this work was presented at 17th Applied Algebra, Algebraic Algorithms, and Error Correcting Codes (AAECC-17), Bangalore,
India, December 16–20, 2007. 相似文献
10.
There are several classes of interior point algorithms that solve linear programming problems in O(√nL) iterations. Among them, several potential reduction algorithms combine both theoretical (O(√nL) iterations) and practical efficiency as they allow the flexibility of line searches in the potential function, and thus
can lead to practical implementations. It is a significant open question whether interior point algorithms can lead to better
complexity bounds. In the present paper we give some negative answers to this question for the class of potential reduction
algorithms. We show that, even if we allow line searches in the potential function, and even for problems that have network
structure, the bound O(√nL) is tight for several potential reduction algorithms, i.e., there is a class of examples with network structure, in which
the algorithms need at least Θ(√nL) iterations to find an optimal solution.
The research of the author was partially supported by a Presidential Young Investigator Award DDM-9158118 with matching funds
from Draper Laboratory. 相似文献
11.
Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in machine
learning, control theory, and discrete geometry. This class of optimization problems, known as rank minimization, is NP-hard,
and for most practical problems there are no efficient algorithms that yield exact solutions. A popular heuristic replaces
the rank function with the nuclear norm—equal to the sum of the singular values—of the decision variable and has been shown
to provide the optimal low rank solution in a variety of scenarios. In this paper, we assess the practical performance of
this heuristic for finding the minimum rank matrix subject to linear equality constraints. We characterize properties of the
null space of the linear operator defining the constraint set that are necessary and sufficient for the heuristic to succeed.
We then analyze linear constraints sampled uniformly at random, and obtain dimension-free bounds under which our null space
properties hold almost surely as the matrix dimensions tend to infinity. Finally, we provide empirical evidence that these
probabilistic bounds provide accurate predictions of the heuristic’s performance in non-asymptotic scenarios. 相似文献
12.
In this paper we study the asymptotic behavior of Bayes estimators for hidden Markov models as the number of observations
goes to infinity. The theorem that we prove is similar to the Bernstein—von Mises theorem on the asymptotic behavior of the
posterior distribution for the case of independent observations. We show that our theorem is applicable to a wide class of
hidden Markov models. We also discuss the implication of the theorem’s assumptions for several models that are used in practical
applications such as ion channel kinetics.
相似文献
13.
Paweł Dłotko Tomasz Kaczynski Marian Mrozek Thomas Wanner 《Discrete and Computational Geometry》2011,46(2):361-388
In this paper we present a new algorithm for computing the homology of regular CW-complexes. This algorithm is based on the
coreduction algorithm due to Mrozek and Batko and consists essentially of a geometric preprocessing algorithm for the standard
chain complex generated by a CW-complex. By employing the concept of S-complexes the original chain complex can—in all known
practical cases—be reduced to a significantly smaller S-complex with isomorphic homology, which can then be computed using
standard methods. Furthermore, we demonstrate that in the context of non-uniform cubical grids this method significantly improves
currently available algorithms based on uniform cubical grids. 相似文献
14.
Oliver Mußhoff Norbert Hirschauer 《Central European Journal of Operations Research》2007,15(2):127-141
In this paper we explore whether the incorporation of systematic time series analyses and mathematical optimization procedures
in the practical planning process has the potential to improve production program decisions. The cases of four German cash
crop farms are investigated over six planning periods. In order to avoid solutions that simply exceed the farmer’s risk tolerance,
the apparently accepted variance of the observed program’s total gross margin is used as an upper bound in the optimization.
For each of the 24 planning occasions, the formal model is used to generate optimized alternative programs. The total gross
margins that could have been realized if the formally optimized programs had been implemented are then compared to those that
were actually realized. We find that the farmers could have increased their total gross margins significantly if—instead of
using simple routines and rules of thumb—they had used adequate methods of statistical analysis combined with the formal optimization
model.
Norbert Hirschauer thanks the German Research Foundation (DFG) for the opportunity to work on this paper during a research
leave. 相似文献
15.
We study qualitative indications for d.c. representations of closed sets in and functions on Hilbert spaces. The first indication
is an index of nonconvexity which can be regarded as a measure for the degree of nonconvexity. We show that a closed set is
weakly closed if this indication is finite. Using this result we can prove the solvability of nonconvex minimization problems.
By duality a minimization problem on a feasible set in which this indication is low, can be reduced to a quasi-concave minimization
over a convex set in a low-dimensional space. The second indication is the separability which can be incorporated in solving
dual problems. Both the index of nonconvexity and the separability can be characteristics to “good” d.c. representations.
For practical computation we present a notion of clouds which enables us to obtain a good d.c. representation for a class
of nonconvex sets. Using a generalized Caratheodory’s theorem we present various applications of clouds. 相似文献
16.
Using an image rectification application arising in the field of forest management, we demonstrate in this paper the practical
feasibility of applying thin plate spline (TPS) techniques to real image warping problems. The use of TPS‐based warping in
large problems can be limited by two factors: numerical instability in the calculation of TPS coefficients, and the intensive
computation involved in evaluating TPS functions. Both drawbacks can be overcome by taking advantage of some recent advances
in the numerical analysis of radial basis functions. Here we relate our experience in applying some of this work to realize
successful TPS warping of large forestry images, and some graphical examples are given. Methods for automated control point
selection and editing are also presented, and a cross‐correlation technique for evaluating the effectiveness of the warps
is described. This experience has guided our development of an effective and efficient software package for control point
selection and TPS warping of digital images.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
17.
Su-Yun Huang Chuhsing Kate Hsiao Ching-Wei Chang 《Annals of the Institute of Statistical Mathematics》2003,55(3):655-670
The article provides a refinement for the volume-corrected Laplace-Metropolis estimator of the marginal likelihood of DiCiccioet al. The correction volume of probability α in DiCiccioet al. is fixed and suggested to take the value α=0.05. In this article α is selected based on an asymptotic analysis to minimize
the mean square relative error (MSRE). This optimal choice of α is shown to be invariant under linear transformations. The
invariance property leads to easy implementation for multivariate problems. An implementation procedure is provided for practical
use. A simulation study and a real data example are presented. 相似文献
18.
An alleged weakness of heuristic optimisation methods is the stochastic character of their solutions: instead of finding the
truly optimal solution, they only provide a stochastic approximation of this optimum. In this paper we look into a particular
application, portfolio optimisation. We demonstrate that the randomness of the ‘optimal’ solution obtained from the algorithm
can be made so small that for all practical purposes it can be neglected. More importantly, we look at the relevance of the
remaining uncertainty in the out-of-sample period. The relationship between in-sample fit and out-of-sample performance is
not monotonous, but still, we observe that up to a point better solutions in-sample lead to better solutions out-of-sample.
Beyond this point there is no more cause for improving the solution any further: any in-sample improvement leads out-of-sample
only to financially meaningless improvements and unpredictable changes (noise) in performance. 相似文献
19.
Marc Hellmuth Wilfried Imrich Werner Klöckl Peter F. Stadler 《Mathematics in Computer Science》2009,2(4):653-682
The practical application of graph prime factorization algorithms is limited in practice by unavoidable noise in the data.
A first step towards error-tolerant “approximate” prime factorization, is the development of local approaches that cover the
graph by factorizable patches and then use this information to derive global factors. We present here a local, quasi-linear
algorithm for the prime factorization of “locally unrefined” graphs with respect to the strong product. To this end we introduce
the backbone
\mathbbB (G)\mathbb{B} (G) for a given graph G and show that the neighborhoods of the backbone vertices provide enough information to determine the global prime factors. 相似文献
20.
In this paper we consider discrete time forward interest rate models. In our approach, unlike in the classical Heath–Jarrow–Morton
framework, the forward rate curves are driven by a random field. Hence we get a general interest rate structure. Our aim is
to give an overview of our results in such a model on the following questions: no-arbitrage conditions, maximum likelihood
estimation of the volatility, as well as the joint estimation of the parameters and the asymptotic behaviour of the estimators,
relationship with continuous models. Finally we give discussion on the practical problems of the estimation and we show several
numerical results on the statistics of such models.
This research has been supported by the Hungarian Scientific Research Fund under Grants No. OTKA–F046061/2004 and OTKA–T048544/2005. 相似文献