共查询到20条相似文献,搜索用时 15 毫秒
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In a series of seminal papers, Thomas J. Stieltjes (1856-1894) gave an elegant electrostatic interpretation for the zeros of classical families of orthogonal polynomials, such as Jacobi, Hermite and Laguerre polynomials. More generally, he extended this approach to the zeros of polynomial solutions of certain second-order linear differential equations (Lamé equations), the so-called Heine-Stieltjes polynomials.In this paper, a class of electrostatic equilibrium problems in R, where the free unit charges x1,…,xn∈R are in presence of a finite family of “attractors” (i.e., negative charges) z1,…,zm∈C?R, is considered and its connection with certain class of Lamé-type equations is shown. In addition, we study the situation when both n→∞ and m→∞, by analyzing the corresponding (continuous) equilibrium problem in presence of a certain class of external fields. 相似文献
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On the numerical solution of a class of Stackelberg problems 总被引:1,自引:0,他引:1
J. V. Outrata 《Mathematical Methods of Operations Research》1990,34(4):255-277
This study tries to develop two new approaches to the numerical solution of Stackelberg problems. In both of them the tools of nonsmooth analysis are extensively exploited; in particular we utilize some results concerning the differentiability of marginal functions and some stability results concerning the solutions of convex programs. The approaches are illustrated by simple examples and an optimum design problem with an elliptic variational inequality.Prepared while the author was visiting the Department of Mathematics, University of Bayreuth as a guest of the FSP Anwendungsbezogene Optimierung und Steuerung. 相似文献
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In this paper, we consider a class of operator equilibrium problems (OEP for short) with operator solutions and derive a Minty type lemma for this class of problems. Further, using this lemma and KKM theorem, we establish some existence theorems for OEP. The theorems presented in this paper generalize, improve and unify many known results. 相似文献
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We consider two classes of generalized monotone functions and generalized skew symmetric functions. By applying the method of auxiliary-principle, we propose and study a predictor-corrector algorithm for solving mixed quasiequilibrium problems involving σ -pseudomonotone functions with respect to a ξ -skew symmetric bifunction, which are concepts introduced in this paper. We prove the convergence of the iterative sequence under generalized pseudomonotonicity and skew symmetry assumptions, improving some known results in the recent literature. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Numerical Algorithms - The article introduces a new algorithm for solving a class of equilibrium problems involving strongly pseudomonotone bifunctions with a Lipschitz-type condition. We describe... 相似文献
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We investigate a class of functional minimization problems with constraints. By means of variational principles, optimal control theory, and numerical methods for nonlinear equations, numerical methods and the corresponding computer software are established to solve the problems. These tools can be used in fitting curves with arbitrary smoothness, different boundary conditions, and constraints. For special boundary conditions, analytical expressions of the curves are derived. Numerical examples are given to demonstrate the effectiveness of the algorithms by the means of curve fitting. 相似文献
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Projection methods are a popular class of methods for solving equilibrium problems. In this paper, we propose approximate one projection methods for solving a class of equilibrium problems, where the cost bifunctions are paramonotone, the feasible sets are defined by a continuous convex function inequality and not necessarily differentiable in the Euclidean space \(\mathcal R^{s}\). At each main iteration step in our algorithms, the usual projections onto the feasible set are replaced by computing inexact subgradients and one projection onto the intersection of two halfspaces containing the solution set of the equilibrium problems. Then, by choosing suitable parameters, we prove convergence of the whole generated sequence to a solution of the problems, under only the assumptions of continuity and paramonotonicity of the bifunctions. Finally, we present some computational examples to illustrate the assumptions of the proposed algorithms. 相似文献
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We consider parametric equilibrium problems in metric spaces. Sufficient conditions for the Hölder calmness of solutions are established. We also study the Hölder well-posedness for equilibrium problems in metric spaces. 相似文献
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Abdellatif Moudafi 《Journal of Global Optimization》2010,47(2):287-292
We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by
a simple proximal method. Under mild conditions, the weak convergence of the sequences generated by the algorithm is obtained.
Using this result we obtain corollaries which improve several corresponding results in this field. 相似文献
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Muhammad Aslam Noor 《Journal of Mathematical Analysis and Applications》2005,312(1):289-299
In this paper, we introduce a new class of equilibrium problems, known as mixed quasi nonconvex equilibrium problems. We suggest some iterative schemes for solving nonconvex equilibrium problems by using the auxiliary principle technique. The convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomonotonicity. As special cases, we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems. 相似文献
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Sz. Gy. Révész 《分析论及其应用》1991,7(3):86-96
In the paper we introduce a class of trigonometrical polynomial extremal problems depending on a continuous parameter 0≤r≤1.
It turns out that the two border cases r=0 and r=1 are known problems investigated earlier by Kamae, Mendes-France, Ruzsa
and the present author. We also introduce another set of extremal problems for measures with similar parametrization, and
prove a duality relationship between the two type of extremal quantities. The proof relies on a minimax theorem proved earlier
by the author. The known duality results are proved as corollaries.
1980 MS Classification. Primary 42A05; Secondary 46B25, 46N05. 相似文献
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Samir Elhedhli 《Operations Research Letters》2005,33(6):615-624
We consider a class of nonlinear knapsack problems with applications in service systems design and facility location problems with congestion. We provide two linearizations and their respective solution approaches. The first is solved directly using a commercial solver. The second is a piecewise linearization that is solved by a cutting plane method. 相似文献
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A. S. Strekalovsky A. V. Orlov A. V. Malyshev 《Numerical Analysis and Applications》2010,3(2):165-173
A quadratic-linear bilevel programming problem is considered. Its optimistic statement is reduced to a series of nonconvex unilevel problems. An approximate algorithm for global search in reduced problems is proposed. Numerical solutions of randomly generated test problems are given and analyzed. 相似文献
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R. B. Vinter 《Journal of Optimization Theory and Applications》1974,13(4):461-483
A class of singular control problems involving amplitude constraints on the controls is examined. IfL
is the space of control functionsU, the control constraint setS can be identified with the unit ball inL
. Now, for anyn (1, ), an analogous problem may be set up withL
n
forU and the unit ball inL
n
forS. This modified problem is necessarily nonsingular for controllable systems. It is shown that, by takingn sufficiently large, the solution to the modified problem also solves the original problem arbitrarily closely (in a sense made precise). Behavior asn is investigated.This research was supported by the Science Research Council of Great Britain and the Commonwealth Fund (Harkness Fellowship). 相似文献