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1.
At each outer iteration of standard Augmented Lagrangian methods one tries to solve a box-constrained optimization problem
with some prescribed tolerance. In the continuous world, using exact arithmetic, this subproblem is always solvable. Therefore,
the possibility of finishing the subproblem resolution without satisfying the theoretical stopping conditions is not contemplated
in usual convergence theories. However, in practice, one might not be able to solve the subproblem up to the required precision.
This may be due to different reasons. One of them is that the presence of an excessively large penalty parameter could impair
the performance of the box-constraint optimization solver. In this paper a practical strategy for decreasing the penalty parameter
in situations like the one mentioned above is proposed. More generally, the different decisions that may be taken when, in
practice, one is not able to solve the Augmented Lagrangian subproblem will be discussed. As a result, an improved Augmented
Lagrangian method is presented, which takes into account numerical difficulties in a satisfactory way, preserving suitable
convergence theory. Numerical experiments are presented involving all the CUTEr collection test problems. 相似文献
2.
Boutheina Ben Yaghlane Khaled Mellouli 《International Journal of Approximate Reasoning》2008,48(2):399-418
Inference algorithms in directed evidential networks (DEVN) obtain their efficiency by making use of the represented independencies between variables in the model. This can be done using the disjunctive rule of combination (DRC) and the generalized Bayesian theorem (GBT), both proposed by Smets [Ph. Smets, Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem, International Journal of Approximate Reasoning 9 (1993) 1–35]. These rules make possible the use of conditional belief functions for reasoning in directed evidential networks, avoiding the computations of joint belief function on the product space. In this paper, new algorithms based on these two rules are proposed for the propagation of belief functions in singly and multiply directed evidential networks. 相似文献
3.
This paper discusses inference for ordered parameters of multinomial distributions. We first show that the asymptotic distributions
of their maximum likelihood estimators (MLEs) are not always normal and the bootstrap distribution estimators of the MLEs
can be inconsistent. Then a class of weighted sum estimators (WSEs) of the ordered parameters is proposed. Properties of the
WSEs are studied, including their asymptotic normality. Based on those results, large sample inferences for smooth functions
of the ordered parameters can be made. Especially, the confidence intervals of the maximum cell probabilities are constructed.
Simulation results indicate that this interval estimation performs much better than the bootstrap approaches in the literature.
Finally, the above results for ordered parameters of multinomial distributions are extended to more general distribution models.
This work was supported by National Natural Science Foundation of China (Grant No. 10371126) 相似文献
4.
An SQP method for general nonlinear programs using only equality constrained subproblems 总被引:5,自引:0,他引:5
P. Spellucci 《Mathematical Programming》1998,82(3):413-448
In this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints. Compared with an older version [P. Spellucci, Han's method without solving QP, in: A. Auslender, W. Oettli, J. Stoer (Eds), Optimization and Optimal Control, Lecture Notes in Control and Information Sciences, vol. 30, Springer, Berlin, 1981, pp. 123–141.] it is much simpler to implement and allows any kind of changes of the working set in every step. Our method relies on a strong regularity condition. As far as it is applicable the new approach is superior to conventional SQP-methods, as demonstrated by extensive numcrical tests. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V. 相似文献
5.
Translated from Issledovaniya po Prikladnoi Matematike, No. 11, Part 1, pp. 11–23, 1984. 相似文献
6.
The two-dimensional wave front shape caused by a point impulse excitation in a
cylindrically anisotropic elastic solid is considered. The elastic parameters of the solid are
constrained such that
E
=
G
This constraint allows the parametric equations of
the wave front to be expressed exactly in terms of elementary transcendental functions. The precise
location of double and cusp points on the front is treated in detail. Time histories of several
wave front patterns are presented and an interesting feature of the front is generalized to the
unconstrained solid. 相似文献
7.
Jonathan Goodman 《Mathematical Programming》1985,33(2):162-171
We derive a quadratically convergent algorithm for minimizing a nonlinear function subject to nonlinear equality constraints. We show, following Kaufman [4], how to compute efficiently the derivative of a basis of the subspace tangent to the feasible surface. The derivation minimizes the use of Lagrange multipliers, producing multiplier estimates as a by-product of other calculations. An extension of Kantorovich's theorem shows that the algorithm maintains quadratic convergence even if the basis of the tangent space changes abruptly from iteration to iteration. The algorithm and its quadratic convergence are known but the drivation is new, simple, and suggests several new modifications of the algorithm. 相似文献
8.
《European Journal of Operational Research》2006,175(1):385-398
A method for combining two types of judgments about an object analyzed, which are elicited from experts, is considered in the paper. It is assumed that the probability distribution of a random variable is known, but its parameters may be determined by experts. The method is based on the use of the imprecise probability theory and allows us to take into account the quality of expert judgments, heterogeneity and imprecision of information supplied by experts. An approach for computing “cautious” expert beliefs under condition that the experts are unknown is studied. Numerical examples illustrate the proposed method. 相似文献
9.
For designing an isotropic inhomogeneous body having a variable elastic modulus and a prescribed shape under the influence of an external force load we give a formulation and solution of the problem of determining the design that is optimal with respect to stress. The problem of optimal design reduces to a certain problem in the theory of elasticity for a non-linearelastic material. As an example we consider the problem of optimal design of an inhomogeneous cylinder. Four figures. Bibliography: 9 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 78–82. 相似文献
10.
In this paper, the problem of estimating parameters of an exponential population is studied under quadratic loss functions. The location parameter of the distribution is assumed to be bounded above by a known constant. Various classes of estimators are derived using integral expression of risk difference (IERD) method of Kubokawa (1994). Some complete class results are also established. 相似文献
11.
Modelling of the forced motions of an elastic beam using the method of integrodifferential relations
G.V. Kostin 《Journal of Applied Mathematics and Mechanics》2013,77(1):57-69
A variational approach to the numerical modelling of forced lateral motions of an Euler–Bernoulli elastic beam is developed for a number of linear boundary conditions using the method of integrodifferential relations. A class of linear boundary actions is considered. A family of quadratic functionals, connecting the displacement field of points of the beam with the bending-moment functions in the cross section and the momentum density is proposed. Variational formulations of the original initial-boundary value problem on the motion of the beam are given and the necessary conditions for the functionals introduced to be stationary are analysed. The integral and local quality characteristics of the admissible approximate solutions are determined. The relation between the variational problems, formulated for the beam model, with the classical Hamilton–Ostrogradskii variational principles is demonstrated. An algorithm for constructing approximate systems of ordinary differential equations is developed, the solution of which yields stationary (minimum) values of the functionals introduced on a specified set of displacement fields, moments and momenta. Examples of calculations of the displacements for an elastic beam and an analysis of the quality of the numerical solutions obtained are presented. 相似文献
12.
In the present paper, the finite-difference method is used for the solution of the direct problem, which enables us to take
into account the diffraction phenomenon on local inhomogeneities of not weak contrast. Examples that allow us to estimate
the precision of restoration of the parameters of such inhomogeneities, depending on the degree of their contrast, are given.
The possibility of restoring the parameters of a local inhomogeneity in a medium containing interfaces with stepwise change
of elastic properties for the case where source and receiver points are located on the free surface is demonstrated. An example
of the numerical estimation of the precision of calculation of a scattered field in the Born approximation, approximating
the wave field by the zero term of the ray method, is offered. Bibliography: 11 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 136–152.
Translated by Yu. V. Kiselev 相似文献
13.
Translated from Issledovaniya po Prikladnoi Matematike, Kazan', No. 14, pp. 25–34, 1987. 相似文献
14.
Shape constrained smoothing using smoothing splines 总被引:1,自引:0,他引:1
Berwin A. Turlach 《Computational Statistics》2005,20(1):81-104
Summary In some regression settings one would like to combine the flexibility of nonparametric smoothing with some prior knowledge
about the regression curve. Such prior knowledge may come from a physical or economic theory, leading to shape constraints
such as the underlying regression curve being positive, monotone, convex or concave. We propose a new method for calculating
smoothing splines that fulfill these kinds of constraints. Our approach leads to a quadratic programming problem and the infinite
number of constraints are replaced by a finite number of constraints that are chosen adaptively. We show that the resulting
problem can be solved using the algorithm of Goldfarb and Idnani (1982, 1983) and illustrate our method on several real data
sets. 相似文献
15.
In this paper, we take advantage of the availability of higher-order derivatives through the table method (see Ref. 1) and suggest a simple variant of the Lagrangian method for constrained optimization. Our method, and the software that we currently have can be used to minimize functions with many variables subject to an arbitrary number of constraints.On leave from the Faculty of Management, Tel Aviv University, Tel Aviv, Israel. 相似文献
16.
Simple ranking method using reference profiles: incremental elicitation of the preference parameters
Khannoussi Arwa Olteanu Alexandru-Liviu Labreuche Christophe Meyer Patrick 《4OR: A Quarterly Journal of Operations Research》2022,20(3):499-530
4OR - The Simple Ranking Method using Reference Profiles (or SRMP) is a Multi-Criteria Decision Aiding technique based on the outranking paradigm, which allows to rank decision alternatives... 相似文献
17.
We study generic constrained differential equations (CDEs) with three parameters, thereby extending Takens's classification of singularities of such equations. In this approach, the singularities analyzed are the Swallowtail, the Hyperbolic, and the Elliptic Umbilics. We provide polynomial local normal forms of CDEs under topological equivalence. Generic CDEs are important in the study of slow–fast (SF) systems. Many properties and the characteristic behavior of the solutions of SF systems can be inferred from the corresponding CDE. Therefore, the results of this paper show a first approximation of the flow of generic SF systems with three slow variables. 相似文献
18.
Aiping Liao 《Computational Optimization and Applications》1993,2(2):129-143
Reduced Hessian methods have been shown to be successful for equality constrained problems. However there are few results on reduced Hessian methods for general constrained problems. In this paper we propose a method for general constrained problems, based on Byrd and Schnabel's basis-independent algorithm. It can be regarded as a smooth extension of the standard reduced Hessian Method.Research supported in part by NSF, AFORS and ONR through NSF grant DMS-8920550. 相似文献
19.
Magnetothermoelastic creep behavior of thick-walled spheres made of functionally graded materials (FGM) placed in uniform magnetic and distributed temperature fields and subjected to an internal pressure is investigated using method of successive elastic solution. The material creep, magnetic and mechanical properties through the radial graded direction are assumed to obey the simple power law variation. Using equations of equilibrium, stress-strain and strain-displacement a differential equation, containing creep strains, for displacement is obtained. A semi-analytical method in conjunction with the Mendelson’s method of successive elastic solution has been developed to obtain history of stresses and strains. History of stresses, strains and effective creep strain rate from their initial elastic distribution at zero time up to 55 years are presented in this paper. Stresses, strains and effective creep strain rate are changing in time with a decreasing rate so that after almost 50 years the time-dependent solution approaches the steady state condition when there is no distinction between stresses and strains at 50 and 55 years. 相似文献
20.
Germana Landi 《Annali dell'Universita di Ferrara》2002,48(1):49-73
In this paper we describe and analyse a numerical method presented by Herskovits for the solution of the nonlinear programming
problem with inequality constraints. We propose some new updating rules for the parameters of the algorithm and show that
these rules are valid and efficient.
Sunto In questo lavoro viene descritto e analizzato un metodo numerico proposto da Herskovits per la soluzione di problemi di minimo non lineari con vincoli di disuguaglianza. In particolare vengono proposte nuove regole per l’aggiornamento dei parametri dell’algoritmo e viene mostrato che tali regole sono valide ed efficienti.相似文献