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1.
In stratified sampling when strata weights are unknown double sampling technique may be used to estimate them. At first a
large simple random sample from the population without considering the stratification is drawn and sampled units belonging
to each stratum are recorded to estimate the unknown strata weights. A stratified random sample is then obtained comprising
of simple random subsamples out of the previously selected units of the strata. If the problem of non-response is there, then
these subsamples may be divided into classes of respondents and non-respondents. A second subsample is then drawn out of non-respondents
and an attempt is made to obtain the information. This procedure is called Double Sampling for Stratification (DSS). Okafor
(Aligarh J Statist 14:13–23, 1994) derived DSS estimators based on the subsampling of non-respondents. Najmussehar and Bari (Aligarh J Statist 22:27–41, 2002) discussed an optimum double sampling design by formulating the problem as a mathematical programming problem and used the
dynamic programming technique to solve it. In the present paper a multivariate stratified population is considered with unknown
strata weights and an optimum sampling design is proposed in the presence of non-response to estimate the unknown population
means using DSS strategy. The problem turns out to be a multiobjective integer nonlinear programming problem. A solution procedure
is developed using Goal Programming technique. A numerical example is presented to illustrate the computational details. 相似文献
2.
Carlos Ansótegui Ramón Béjar Cèsar Fernández Carla Gomes Carles Mateu 《Journal of Heuristics》2011,17(5):589-614
Sudoku problems are some of the most known and enjoyed pastimes, with a never diminishing popularity, but, for the last few
years those problems have gone from an entertainment to an interesting research area, a twofold interesting area, in fact.
On the one side Sudoku problems, being a variant of Gerechte Designs and Latin Squares, are being actively used for experimental
design, as in Bailey et al. (Am. Math. Mon. 115:383–404, 2008; J. Agron. Crop Sci. 165:121–130, 1990), Morgan (Latin squares and related experimental designs. Wiley, New York, 2008) and Vaughan (Electron. J. Comb. 16, 2009). On the other hand, Sudoku problems, as simple as they seem, are really hard structured combinatorial search problems, and
thanks to their characteristics and behavior, they can be used as benchmark problems for refining and testing solving algorithms
and approaches. Also, thanks to their high inner structure, their study can contribute more than studies of random problems
to our goal of solving real-world problems and applications and understanding problem characteristics that make them hard
to solve. In this work we use two techniques for solving and modeling Sudoku problems, namely, Constraint Satisfaction Problem
(CSP) and Satisfiability Problem (SAT) approaches. To this effect we define the Generalized Sudoku Problem (GSP), where regions
can be of rectangular shape, problems can be of any order, and solution existence is not guaranteed. With respect to the worst-case
complexity, we prove that GSP with block regions of m rows and n columns with m≠n is NP-complete. For studying the empirical hardness of GSP, we define a series of instance generators, that differ in the
balancing level they guarantee between the constraints of the problem, by finely controlling how the holes are distributed
in the cells of the GSP. Experimentally, we show that the more balanced are the constraints, the higher the complexity of
solving the GSP instances, and that GSP is harder than the Quasigroup Completion Problem (QCP), a problem generalized by GSP.
Finally, we provide a study of the correlation between backbone variables—variables with the same value in all the solutions
of an instance—and hardness of GSP. 相似文献
3.
In the multiple-output regression context, Hallin et al. (Ann Statist 38:635–669, 2010) introduced a powerful data-analytical tool based on regression quantile regions. However, the computation of these regions, that are obtained by considering in all directions an original concept of directional
regression quantiles, is a very challenging problem. Paindaveine and Šiman (Comput Stat Data Anal 2011b) described a first elegant solution relying on linear programming techniques. The present paper provides another solution
based on the fact that the quantile regions can also be computed from a competing concept of projection regression quantiles, elaborated in Kong and Mizera (Quantile tomography: using quantiles with multivariate data 2008) and Paindaveine and Šiman (J Multivar Anal 2011a). As a by-product, this alternative solution further provides various characteristics useful for statistical inference. We
describe in detail the algorithm solving the parametric programming problem involved, and illustrate the resulting procedure
on simulated data. We show through simulations that the Matlab implementation of the algorithm proposed in this paper is faster than that from Paindaveine and Šiman (Comput Stat Data Anal
2011b) in various cases. 相似文献
4.
We consider a two-phase problem in thermal conductivity: inclusions filled with a material of conductivity σ
1 are layered in a body of conductivity σ
2. We address the shape sensitivity of the first eigenvalue associated with Dirichlet boundary conditions when both the boundaries
of the inclusions and the body can be modified. We prove a differentiability result and provide the expressions of the first
and second order derivatives. We apply the results to the optimal design of an insulated body. We prove the stability of the
optimal design thanks to a second order analysis. We also continue the study of an extremal eigenvalue problem for a two-phase
conductor in a ball initiated by Conca et al. (Appl. Math. Optim. 60(2):173–184, 2009) and pursued in Conca et al. (CANUM 2008, ESAIM Proc., vol. 27, pp. 311–321, EDP Sci., Les Ulis, 2009). 相似文献
5.
Karsten Eppler Helmut Harbrecht Mario S. Mommer 《Computational Optimization and Applications》2008,40(2):281-298
The present paper is concerned with investigating the capability of the smoothness preserving fictitious domain method from
Mommer (IMA J. Numer. Anal. 26:503–524, 2006) to shape optimization problems. We consider the problem of maximizing the Dirichlet energy functional in the class of all
simply connected domains with fixed volume, where the state equation involves an elliptic second order differential operator
with non-constant coefficients. Numerical experiments in two dimensions validate that we arrive at a fast and robust algorithm
for the solution of the considered class of problems. The proposed method can be applied to three dimensional shape optimization
problems. 相似文献
6.
Rani Yadav 《Annali dell'Universita di Ferrara》2012,58(1):217-227
In the year 1994, Gupta (Approx Theory Appl (N.S.) 10(3):74–78, 1994) introduced the integral modification of well known Baskakov operators with weights of Beta basis functions and obtained
better approximation over the usual Baskakov Durrmeyer operators. The rate of convergence for Bézier variant of these operators
for functions of bounded variations were discussed in Gupta (Int J Math Math Sci 32(8):471–479, 2002). The present paper is the extension of the previous work, here we consider the Bézier variant of Baskakov-Beta-Stancu operators.
We estimate the rate of convergence of these operators for the bounded functions. In the end of the paper we suggest an open
problem. 相似文献
7.
The matrix rank minimization problem has applications in many fields, such as system identification, optimal control, low-dimensional
embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization problem, is often
solved instead. Recently, Ma, Goldfarb and Chen proposed a fixed-point continuation algorithm for solving the nuclear norm
minimization problem (Math. Program., doi:, 2009). By incorporating an approximate singular value decomposition technique in this algorithm, the solution to the matrix rank
minimization problem is usually obtained. In this paper, we study the convergence/recoverability properties of the fixed-point
continuation algorithm and its variants for matrix rank minimization. Heuristics for determining the rank of the matrix when
its true rank is not known are also proposed. Some of these algorithms are closely related to greedy algorithms in compressed
sensing. Numerical results for these algorithms for solving affinely constrained matrix rank minimization problems are reported. 相似文献
8.
It is of general knowledge that those (ultra)filter convergence relations coming from a topology can be characterized by two
natural axioms. However, the situation changes considerable when moving to sequential spaces. In case of unique limit points
Kisyński (Colloq Math 7:205–211, 1959/1960) obtained a result for sequential convergence similar to the one for ultrafilters, but the general case seems more difficult
to deal with. Finally, the problem was solved by Koutnik (Closure and topological sequential convergence. In: Convergence
Structures 1984 (Bechyně, 1984). Math. Res., vol. 24, pp. 199–204. Akademie-Verlag, Berlin, 1985). In this paper we present an alternative approach to this problem. Our goal is to find a characterization more closely related
to the case of ultrafilter convergence. We extend then the result to characterize sequential convergence relations corresponding
to Fréchet topologies, as well to those corresponding to pretopological spaces.
相似文献
9.
Cedric Boutillier Sevak Mkrtchyan Nicolai Reshetikhin Peter Tingley 《Annales Henri Poincare》2012,13(2):271-296
Random skew plane partitions of large size distributed according to an appropriately scaled Schur process develop limit shapes.
In the present work, we consider the limit of large random skew plane partitions where the inner boundary approaches a piecewise
linear curve with non-lattice slopes, describing the limit shape and the local fluctuations in various regions. This analysis
is fairly similar to that in Okounkov and Reshetikhin (Commun Math Phys 269:571–609, 2007), but we do find some new behavior. For instance, the boundary of the limit shape is now a single smooth (not algebraic)
curve, whereas the boundary in Okounkov and Reshetikhin (Commun Math Phys 269:571–609, 2007) is singular. We also observe the bead process introduced in Boutillier (Ann Probab 37(1):107–142, 2009) appearing in the asymptotics at the top of the limit shape. 相似文献
10.
L. C. Ceng S. Schaible J. C. Yao 《Journal of Optimization Theory and Applications》2008,139(2):403-418
We introduce an implicit iteration scheme with a perturbed mapping for finding a common element of the set of solutions of
an equilibrium problem and the set of common fixed points of finitely many nonexpansive mappings in a Hilbert space. Then,
we establish some convergence theorems for this implicit iteration scheme which are connected with results by Xu and Ori (Numer.
Funct. Analysis Optim. 22:767–772, 2001), Zeng and Yao (Nonlinear Analysis, Theory, Methods Appl. 64:2507–2515, 2006) and Takahashi and Takahashi (J. Math. Analysis Appl. 331:506–515, 2007). In particular, necessary and sufficient conditions for strong convergence of this implicit iteration scheme are obtained.
In this research, the first author was partially supported by the National Science Foundation China (10771141), Ph.D. Program
Foundation of Ministry of Education of China (20070270004), and Science and Technology Commision of Shanghai Municipality
Grant (075105118). 相似文献
11.
A procedure for the construction of robust, upper bounds for the error in the finite element approximation of singularly perturbed
reaction–diffusion problems was presented in Ainsworth and Babuška (SIAM J Numer Anal 36(2):331–353, 1999) which entailed the solution of an infinite dimensional local boundary value problem. It is not possible to solve this problem
exactly and this fact was recognised in the above work where it was indicated that the limitation would be addressed in a
subsequent article. We view the present work as fulfilling that promise and as completing the investigation begun in Ainsworth
and Babuška (SIAM J Numer Anal 36(2):331–353, 1999) by removing the obligation to solve a local problem exactly. The resulting new estimator is indeed fully computable and
the first to provide fully computable, robust upper bounds in the setting of singularly perturbed problems discretised by
the finite element method. 相似文献
12.
We present a rigorous analysis of the performance of some one-step discretization schemes for a class of PT-symmetric singular
boundary eigenvalue problem which encompasses a number of different problems whose investigation has been inspired by the
2003 article of Benilov et al. (J Fluid Mech 497:201–224, 2003). These discretization schemes are analyzed as initial value problems rather than as discrete boundary problems, since this
is the setting which ties in most naturally with the formulation of the problem which one is forced to adopt due to the presence
of an interior singularity. We also devise and analyze a variable step scheme for dealing with the singular points. Numerical
results show better agreement between our results and those obtained from small-ϵ asymptotics than has been shown in results presented hitherto. 相似文献
13.
14.
The quickest path problem is related to the classical shortest path problem, but its objective function concerns the transmission
time of a given amount of data throughout a path, which involves both cost and capacity. The K-quickest simple paths problem generalises the latter, by looking for a given number K of simple paths in non-decreasing order of transmission time.
Two categories of algorithms are known for ranking simple paths according to the transmission time. One is the adaptation
of deviation algorithms for ranking shortest simple paths (Pascoal et al. in Comput. Oper. Res. 32(3):509–520, 2005; Rosen et al. in Comput. Oper. Res. 18(6):571–584, 1991), and another is based on ranking shortest simple paths in a sequence of networks with fixed capacity lower bounds (Chen
in Inf. Process. Lett. 50:89–92, 1994), and afterwards selecting the K quickest ones.
After reviewing the quickest path and the K-quickest simple paths problems we describe a recent algorithm for ranking quickest simple paths (Pascoal et al. in Ann. Oper.
Res. 147(1):5–21, 2006). This is a lazy version of Chen’s algorithm, able to interchange the calculation of new simple paths and the output of each
k-quickest simple path.
Finally, the described algorithm is computationally compared to its former version, as well as to deviation algorithms.
相似文献
15.
New approach for the nonlinear programming with transient stability constraints arising from power systems 总被引:1,自引:0,他引:1
Xiaojiao Tong Soon-Yi Wu Renjun Zhou 《Computational Optimization and Applications》2010,45(3):495-520
This paper presents a new approach for solving a class of complicated nonlinear programming problems arises from optimal power
flow with transient stability constraints (denoted by OTS) in power systems. By using a functional transformation technology
proposed in Chen et al. (IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 48:327–339, [2001]), the OTS problem is transformed to a semi-infinite programming (SIP). Then based on the KKT (Karush-Kuhn-Tucker) system
of the reformulated SIP problem and the finite approximation technology, an iterative method is presented, which develops
Wu-Li-Qi-Zhou’ (Optim. Methods Softw. 20:629–643, [2005]) method. In order to save the computing cost, some typical computing technologies, such as active set strategy, quasi-Newton
method for the subproblems coming from the finite approximation model, are addressed. The global convergence of the proposed
algorithm is established. Numerical examples from power systems are tested. The computing results show the efficiency of the
new approach. 相似文献
16.
Michael B. Freimer Jeffrey T. Linderoth Douglas J. Thomas 《Computational Optimization and Applications》2012,51(1):51-75
Stochastic linear programs can be solved approximately by drawing a subset of all possible random scenarios and solving the
problem based on this subset, an approach known as sample average approximation (SAA). The value of the objective function
at the optimal solution obtained via SAA provides an estimate of the true optimal objective function value. This estimator
is known to be optimistically biased; the expected optimal objective function value for the sampled problem is lower (for
minimization problems) than the optimal objective function value for the true problem. We investigate how two alternative
sampling methods, antithetic variates (AV) and Latin Hypercube (LH) sampling, affect both the bias and variance, and thus
the mean squared error (MSE), of this estimator. For a simple example, we analytically express the reductions in bias and
variance obtained by these two alternative sampling methods. For eight test problems from the literature, we computationally
investigate the impact of these sampling methods on bias and variance. We find that both sampling methods are effective at
reducing mean squared error, with Latin Hypercube sampling outperforming antithetic variates. For our analytic example and
the eight test problems we derive or estimate the condition number as defined in Shapiro et al. (Math. Program. 94:1–19, 2002). We find that for ill-conditioned problems, bias plays a larger role in MSE, and AV and LH sampling methods are more likely
to reduce bias. 相似文献
17.
We consider a class of unconstrained nonsmooth convex optimization problems, in which the objective function is the sum of
a convex smooth function on an open subset of matrices and a separable convex function on a set of matrices. This problem
includes the covariance selection problem that can be expressed as an ℓ
1-penalized maximum likelihood estimation problem. In this paper, we propose a block coordinate gradient descent method (abbreviated
as BCGD) for solving this class of nonsmooth separable problems with the coordinate block chosen by a Gauss-Seidel rule. The
method is simple, highly parallelizable, and suited for large-scale problems. We establish global convergence and, under a
local Lipschizian error bound assumption, linear rate of convergence for this method. For the covariance selection problem,
the method can terminate in O(n3/e){O(n^3/\epsilon)} iterations with an e{\epsilon}-optimal solution. We compare the performance of the BCGD method with the first-order methods proposed by Lu (SIAM J Optim
19:1807–1827, 2009; SIAM J Matrix Anal Appl 31:2000–2016, 2010) for solving the covariance selection problem on randomly generated instances. Our numerical experience suggests that the
BCGD method can be efficient for large-scale covariance selection problems with constraints. 相似文献
18.
In this paper we analyze the hydrodynamic equations for Ginzburg–Landau vortices as derived by E (Phys. Rev. B. 50(3):1126–1135,
1994). In particular, we are interested in the mean field model describing the evolution of two patches of vortices with equal
and opposite degrees. Many results are already available for the case of a single density of vortices with uniform degree.
This model does not take into account the vortex annihilation, hence it can also be seen as a particular instance of the signed
measures system obtained in Ambrosio et al. (Ann. Inst. H. Poincaré Anal. Non Linéaire 28(2):217–246, 2011) and related to the Chapman et al. (Eur. J. Appl. Math. 7(2):97–111, 1996) formulation. We establish global existence of L
p
solutions, exploiting some optimal transport techniques introduced in this context in Ambrosio and Serfaty (Commun. Pure
Appl. Math. LXI(11):1495–1539, 2008). We prove uniqueness for L
∞ solutions, as expected by analogy with the incompressible Euler equations in fluidodynamics. We also consider the corresponding
Dirichlet problem in a bounded domain. Moreover, we show some simple examples of 1-dimensional dynamic. 相似文献
19.
M. V. Shamolin 《Journal of Mathematical Sciences》2009,161(5):734-778
The results of the presented work are due to the study of the applied problem of the rigid body motion in a resisting medium;
see [210, 211], where complete lists of transcendental first integrals expressed through a finite combination of elementary functions were
obtained. This circumstance allowed the author to perform a complete analysis of all phase trajectories and highlight those
properties of them which exhibit the roughness and preserve for systems of a more general form. The complete integrability of those systems is related to symmetries of
a latent type. Therefore, it is of interest to study sufficiently wide classes of dynamical systems having analogous latent
symmetries.
As is known, the concept of integrability is sufficiently broad and undeterminate in general. In its construction, it is necessary
to take into account in what sense it is understood (it is meant that a certain criterion according to which one makes a conclusion
that the structure of trajectories of the dynamical system considered is especially “attractive and simple”), in which function
classes the first integrals are sought for, etc. (see also [1, 4, 14, 17, 20–22, 35, 40–42, 47, 83–85, 117, 120]). 相似文献
20.
It is known that the set of all solutions of a commutant lifting and other interpolation problems admits a Redheffer linear-fractional
parametrization. The method of unitary coupling identifies solutions of the lifting problem with minimal unitary extensions
of a partially defined isometry constructed explicitly from the problem data. A special role is played by a particular unitary
extension, called the central or universal unitary extension. The coefficient matrix for the Redheffer linear-fractional map has a simple expression in terms of the universal unitary
extension. The universal unitary extension can be seen as a unitary coupling of four unitary operators (two bilateral shift
operators together with two unitary operators coming from the problem data) which has special geometric structure. We use
this special geometric structure to obtain an inverse theorem (Theorem 8.4) which characterizes the coefficient matrices for
a Redheffer linear-fractional map arising in this way from a lifting problem. The main tool is the formalism of unitary scattering
systems developed in Boiko et al. (Operator theory, system theory and related topics (Beer-Sheva/Rehovot 1997), pp. 89–138,
2001) and Kheifets (Interpolation theory, systems theory and related topics, pp. 287–317, 2002) 相似文献