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Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets

IEEE TRANSACTIONS ON POWER SYSTEMS 2004年第1期19卷 195-206页

作者： Contreras, J Klusch, M Krawczyk, JB Univ Castilla La Mancha Escuela Tecn Super Ingn Ind E-13071 Ciudad Real Spain German Res Ctr Artificial Intelligence D-66123 Saarbrucken Germany Victoria Univ Wellington Sch Econ & Finance Wellington 6000 New Zealand

A numerical method based on a relaxation algorithm and the Nikaido-Isoda function is presented for the calculation of Nash-Cournot equilibria in electricity markets. Nash equilibrium is attained through a relaxation procedure applied to an objective function, the Nikaido-Isoda function, which is derived from the existing profit maximization functions calculated by the generating companies. We also show how to use the relaxation algorithm to compute, and enforce, a coupled constraint equilibrium, which occurs if regulatory, generation, and distribution (and more) restrictions are placed on the companies and entire markets. Moreover, we use the relaxation algorithm to compute players' payoffs under several player configurations. This is needed for the solution of our game under cooperative game theory concepts, such as the bilateral Shapley value and the kernel. We show that the existence of both depends critically on demand price elasticity. The numerical method converges to a unique solution under rather specific but plausible concavity conditions. A case study from the IEEE 30-bus system, and a three-bus bilateral market example with a dc model of the transmission line constraints are presented and discussed.

关键词： bilateral Shapley value coalition formation coupled constraints electricity markets kernel Nash-Cournot equilibrium Nikaido-Isoda function relaxation algorithm

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Weak and strong convergence of inertial Tseng's extragradient algorithms for solving variational inequality problems

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OPTIMIZATION 2021年第5-6期70卷 1195-1216页

作者： Fan, Jingjing Qin, Xiaolong Univ Elect Sci & Technol China Inst Fundamental & Frontier Sci Chengdu Peoples R China

In this paper, we introduce two inertial Tseng's extragradient algorithms with the Armijo-like step size rule for solving variational inequality problems involving monotone and Lipschitz continuous operators. Strong and weak convergence theorems are established in Hilbert spaces. Some numerical experiments are provided to illustrate the efficiency and advantage of the proposed algorithms.

关键词： Variational inequality problem Tseng's extragradient method inertial method relaxation algorithm Armijo-like step size rule

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AMlet, RAMlet, and GAMlet: Automatic nonlinear fitting of additive models, robust and generalized, with wavelets

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2004年第2期13卷 283-309页

作者： Sardy, S Tseng, P Swiss Fed Inst Technol Dept Math CH-1015 Lausanne Switzerland Univ Washington Dept Math Seattle WA 98195 USA

A simple and yet powerful method is presented to estimate nonlinearly and nonparametrically the components of additive models using wavelets. The estimator enjoys the good statistical and computational properties of the Waveshrink scatterplot smoother and it can be efficiently computed using the block coordinate relaxation optimization technique. A rule for the automatic selection of the smoothing parameters, suitable for data mining of large datasets, is derived. The wavelet-based method is then extended to estimate generalized additive models. A primal-dual log-barrier interior point algorithm is proposed to solve the corresponding convex programming problem. Based on an asymptotic analysis, a rule for selecting the smoothing parameters is derived, enabling the estimator to be fully automated in practice. We illustrate the finite sample property with a Gaussian and a Poisson simulation.

关键词： (generalized) additive models convex programming data mining interiorpoint algorithm regularized likelihood relaxation algorithm signal denoising universal smoothing parameter

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FINDING A GOOD FIGURE THAT APPROXIMATELY PASSES THROUGH GIVEN POINTS

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PATTERN RECOGNITION 1980年第5期12卷 319-326页

作者： SLAGLE, JR DIXON, JK Naval Research Laboratory Washington D.C. 20375 U.S.A

A system is presented which, when given a list of points on the plane, will find a good figure to approximately pass through the points. Some of the thirteen figures considered are the line segment, circle, parallelogram, and equilateral triangle. The system searches a disjunctive (or) goal tree. We are performing research needed in the development of a robot manipulator system. Object recognition is a very important part of the system. Although the robot will be sensing three-dimensional objects from tactile or other sensors, there are reasons for first treating the two-dimensional case.

关键词： Object recognition relaxation algorithm Figure network Goal tree Robot manipulator Tactile sensor

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Coupled constraint Nash equilibria in environmental games

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RESOURCE AND ENERGY ECONOMICS 2005年第2期27卷 157-181页

作者： Krawczyk, JB Victoria Univ Wellington Wellington New Zealand

The focus of this paper is on how to model and solve an environmental compliance problem using [Rosen, J.B., 1965. Existence and uniqueness of equilibrium points for concave n-person games. Econometrica 33 (3), 520-534] seminal idea of coupled constraint equilibrium. First, Rosen's results about the existence and uniqueness of a Nash normalised equilibrium for coupled constraint games are explained. These results are then combined with a numerical approach to game solutions based on the Nikaido-Isoda function. A river basin pollution game, which is a model for a common nonpoint source pollution problem, is solved numerically using this approach. In the game, the agents face a joint constraint on the total pollution, which defines a coupled constraint set in the combined strategy space. This makes the game special in terms of the strategy spaces. Unlike for standard games where they are defined separately for each player, here we have a joint constraint on the combined strategy space of all players. Hence, the game needs coupled constraint equilibrium as the solution concept. Static and (open-loop) dynamic equilibria are computed for the basin problem under the discussed equilibrium concept. All equilibria are instructive for the legislator, in that they contain information on how to choose the "optimal" charges, under which agents obey the constraints. (c) 2004 Elsevier B.V. All rights reserved.

关键词： compliance problem nonpoint-source pollution computational economics rosen coupled constraint games open-loop equilibrium Nikado-Isoda function relaxation algorithm

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ACCELERATING WILSON FERMION MATRIX INVERSIONS BY MEANS OF THE STABILIZED BICONJUGATE GRADIENT algorithm

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C-PHYSICS AND COMPUTERS 1994年第6期5卷 1073-1088页

作者： FROMMER, A HANNEMANN, V NOCKEL, B LIPPERT, T SCHILLING, K UNIV GESAMTHSCH WUPPERTAL DEPT PHYSD-42097 WUPPERTALGERMANY

The stabilized biconjugate gradient algorithm BiCGStab recently presented by van der Vorst is applied to the inversion of the lattice fermion operator in the Wilson formulation of lattice Quantum Chromodynamics. Its computational efficiency is tested in a comparative study against the conjugate gradient and minimal, residual methods. Both for quenched gauge configurations at beta = 6.0 and gauge configurations with dynamical fermions at beta = 5.4, we find BiCGStab to be superior to the other methods. BiCGStab turns out to be particularly useful in the chiral regime of small quark masses.

关键词： LATTICE QCD relaxation algorithm PARALLEL COMPUTER

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The relaxation normal form of braids is regular

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INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION 2017年第1期27卷 61-105页

作者： Juge, Vincent PSL Res Univ Mines ParisTech F-75272 Paris 06 France Univ Paris Diderot Sorbonne Paris Cite CNRS IRIFUMR 8243 F-75205 Paris France Univ Paris Saclay CNRS LSV Paris France Univ Paris Saclay ENS Cachan Paris France

Braids can be represented geometrically as laminations of punctured disks. The geometric complexity of a braid is the minimal complexity of a lamination that represents it, and tight laminations are representatives of minimal complexity. These laminations give rise to a normal form of braids, via a relaxation algorithm. We study here this relaxation algorithm and the associated normal form. We prove that this normal form is regular and prefix-closed. We provide an effective construction of a deterministic automaton that recognizes this normal form.

关键词： Braid group lamination relaxation algorithm regular normal form

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relaxation methods for solving the tensor equation arising from the higher-order Markov chains

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NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 2019年第5期26卷 e2260-e2260页

作者： Liu, Dongdong Li, Wen Vong, Seak-Weng Univ Macau Fac Sci & Technol Dept Math Macau Peoples R China Guangdong Univ Technol Sch Appl Math Guangzhou Guangdong Peoples R China South China Normal Univ Sch Math Sci Guangzhou 510631 Guangdong Peoples R China

In this paper, we propose several relaxation algorithms for solving the tensor equation arising from the higher-order Markov chain and the multilinear PageRank. The semi-symmetrization technique on the original equation is also employed to modify the proposed algorithms. The convergence analysis is given for the proposed algorithms. It is shown that the new algorithms are more efficient than the existing ones by some numerical experiments when relaxation parameters are chosen suitably.

关键词： higher-order Markov chain multilinear PageRank relaxation algorithm tensor equation

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Many masses on one stroke: Economic computation of quark propagators

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C 1995年第5期6卷 627-638页

作者： Frommer, A Nockel, B Gusken, S Lippert, T Schilling, K UNIV GESAMTHSCH WUPPERTAL DEPT PHYS D-42097 WUPPERTAL GERMANY FORSCHUNGSZENTRUM JULICH HLRZ DESY D-52425 JULICH GERMANY

The computational effort in the calculation of Wilson fermion quark propagators in Lattice Quantum Chromodynamics can be considerably reduced by exploiting the Wilson fermion matrix structure in inversion algorithms based on the non-symmetric Lanczos process. We consider two such methods: QMR (quasi minimal residual) and BCG (biconjugate gradients). Based on the decomposition M/kappa = 1/kappa-D of the Wilson mass matrix, using QMR, one can carry out inversions on a whole trajectory of masses simultaneously, merely at the computational expense of a single propagator computation. In other words, one has to compute the propagator corresponding to the lightest mass only, while all the heavier masses are given for free, at the price of extra storage. Moreover, the symmetry gamma 5 M = M(+) gamma 5 can be used to cut the computational effort in QMR and BCG by a factor of two. We show that both methods then become - in the critical regime of small quark masses - competitive to BiCGStab and significantly better than the standard MR method, with optimal relaxation factor, and CG as applied to the normal equations.

关键词： lattice QCD relaxation algorithm parallel computer

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Game-theoretic Approach of Fair Bandwidth Allocation in DVB-RCS Networks

Game-theoretic Approach of Fair Bandwidth Allocation in DVB-...

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International Workshop on Satellite and Space Communications

作者： Vassaki, Stavroula Panagopoulos, Athanasios D. Constantinou, Philip Natl Tech Univ Athens ICCS Mobile Radio Commun Lab Sch Elect & Comp Engn GR-15780 Athens Greece

ISBN: (纸本)9781424443840

In the present paper we study the problem of bandwidth allocation in DVB-RCS networks. DVB-RCS networks operate at Ku band and above. At these frequencies, rain attenuation is the dominant fading mechanism and exhibits significant spatial-temporal variation among the users. Firstly, the resource allocation is modeled as a non cooperative game and we find the Nash equilibrium employing the Nikaido-Isoda function and a relaxation algorithm. Moreover, we force the game to converge to a more fair equilibrium point, by introducing a pricing scheme. The bandwidth allocation to users that are affected more by rain fading is improved. Finally, we apply the principles of a cooperative game to describe the problem of resource allocation and we compare the results of the three approaches. Some useful conclusions are drawn.

关键词： DVB-RCS bandwidth allocation game theory Nikaido-Isoda function relaxation algorithm nash bargaining

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