Distributed accelerated Nash equilibrium learning for two-subnetwork zero-sum game with bilinear coupling

Xianlin Zeng; Lihua Dou; Jinqiang Cui

Displaying similar documents to “Distributed accelerated Nash equilibrium learning for two-subnetwork zero-sum game with bilinear coupling”

On the weighted Euclidean matching problem in $ℝ^{d}$

Birgit Anthes, Ludger Rüschendorf (2001)

Applicationes Mathematicae

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A partitioning algorithm for the Euclidean matching problem in $ℝ^{d}$ is introduced and analyzed in a probabilistic model. The algorithm uses elements from the fixed dissection algorithm of Karp and Steele (1985) and the Zig-Zag algorithm of Halton and Terada (1982) for the traveling salesman problem. The algorithm runs in expected time $n {(l o g n)}^{p - 1}$ and approximates the optimal matching in the probabilistic sense.

A descent algorithm for $ε$ - approximation of continuous functions with values in unitary space

M. Janc (1982)

Matematički Vesnik

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Safe consensus control of cooperative-competitive multi-agent systems via differential privacy

Jiayue Ma, Jiangping Hu (2022)

Kybernetika

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This paper investigates a safe consensus problem for cooperative-competitive multi-agent systems using a differential privacy (DP) approach. Considering that the agents simultaneously interact cooperatively and competitively, we propose a novel DP bipartite consensus algorithm, which guarantees that the DP strategy only works on competitive pairs of agents. We then prove that the proposed algorithm can achieve the mean square bipartite consensus and $(p, r)$ -accuracy. Furthermore, a differential...

Equilibrium analysis of distributed aggregative game with misinformation

Meng Yuan, Zhaoyang Cheng, Te Ma (2024)

Kybernetika

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This paper considers a distributed aggregative game problem for a group of players with misinformation, where each player has a different perception of the game. Player’s deception behavior is inevitable in this situation for reducing its own cost. We utilize hypergame to model the above problems and adopt $ϵ$ -Nash equilibrium for hypergame to investigate whether players believe in their own cognition. Additionally, we propose a distributed deceptive algorithm for a player implementing...

The general methods of finding the sum $S_{n}$ for all kinds of series

K. Orlov (1981)

Matematički Vesnik

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The adaptation of the $k$ -means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm

Rudolf Scitovski, Kristian Sabo (2019)

Applications of Mathematics

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We consider the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance, whereby an ellipse $E$ is viewed as a Mahalanobis circle with center $S$ , radius $r$ , and some positive definite matrix $Σ$ . A very efficient method for solving this problem is proposed. The method uses a modification of the $k$ -means algorithm for Mahalanobis-circle centers. The initial approximation consists of the set of circles whose centers...

A stochastic mirror-descent algorithm for solving $A X B = C$ over an multi-agent system

Yinghui Wang, Songsong Cheng (2021)

Kybernetika

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In this paper, we consider a distributed stochastic computation of $A X B = C$ with local set constraints over an multi-agent system, where each agent over the network only knows a few rows or columns of matrixes. Through formulating an equivalent distributed optimization problem for seeking least-squares solutions of $A X B = C$ , we propose a distributed stochastic mirror-descent algorithm for solving the equivalent distributed problem. Then, we provide the sublinear convergence of the proposed algorithm....

An improvement of Euclid's algorithm

Zítko, Jan, Kuřátko, Jan

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The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid’s algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using $c$ - $s$ transformation and $Q R$ -factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.

Uniform convergence of the greedy algorithm with respect to the Walsh system

Martin Grigoryan (2010)

Studia Mathematica

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For any 0 < ϵ < 1, p ≥ 1 and each function $f \in L^{p} [0, 1]$ one can find a function $g \in L^{\infty} [0, 1)$ with mesx ∈ [0,1): g ≠ f < ϵ such that its greedy algorithm with respect to the Walsh system converges uniformly on [0,1) and the sequence $| c_{k} (g) | : k \in s p e c (g)$ is decreasing, where $c_{k} (g)$ is the sequence of Fourier coefficients of g with respect to the Walsh system.

A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space

L.O. Jolaoso, H.A. Abass, O.T. Mewomo (2019)

Archivum Mathematicum

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In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of $δ$ -demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition $\sum_{n = 1}^{\infty} β_{n} ∥ x_{n - 1} - x_{n} ∥ < + \infty$ on the inertial term. Finally,...

An interior-point algorithm for semidefinite least-squares problems

Chafia Daili, Mohamed Achache (2022)

Applications of Mathematics

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We propose a feasible primal-dual path-following interior-point algorithm for semidefinite least squares problems (SDLS). At each iteration, the algorithm uses only full Nesterov-Todd steps with the advantage that no line search is required. Under new appropriate choices of the parameter $β$ which defines the size of the neighborhood of the central-path and of the parameter $θ$ which determines the rate of decrease of the barrier parameter, we show that the proposed algorithm is well defined...

An adaptive $s$ -step conjugate gradient algorithm with dynamic basis updating

Erin Claire Carson (2020)

Applications of Mathematics

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The adaptive $s$ -step CG algorithm is a solver for sparse symmetric positive definite linear systems designed to reduce the synchronization cost per iteration while still achieving a user-specified accuracy requirement. In this work, we improve the adaptive $s$ -step conjugate gradient algorithm by the use of iteratively updated estimates of the largest and smallest Ritz values, which give approximations of the largest and smallest eigenvalues of $A$ , using a technique due to G. Meurant and...

New hybrid conjugate gradient method for nonlinear optimization with application to image restoration problems

Youcef Elhamam Hemici, Samia Khelladi, Djamel Benterki (2024)

Kybernetika

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The conjugate gradient method is one of the most effective algorithm for unconstrained nonlinear optimization problems. This is due to the fact that it does not need a lot of storage memory and its simple structure properties, which motivate us to propose a new hybrid conjugate gradient method through a convex combination of $β_{k}^{R M I L}$ and $β_{k}^{H S}$ . We compute the convex parameter $θ_{k}$ using the Newton direction. Global convergence is established through the strong Wolfe conditions. Numerical experiments...

Implicitization of Parametric Hypersurfaces via Points

Ferruccio Orecchia, Isabella Ramella (2018)

Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche

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Given a parametric polynomial representation of an algebraic hypersurface $\mathbf{S}$ in the projective space we give a new algorithm for finding the implicit cartesian equation of $\mathbf{S}$ .The algorithm is based on finding a suitable finite number of points on $\mathbf{S}$ and computing, by linear algebra, the equation of the hypersurface of least degree that passes through the points. In particular the algorithm works for plane curves and surfaces in the ordinary three-dimensional space. Using C++ the algorithm...