In this article, we introduce an inertial projection and contraction algorithm by combining inertial type algorithms with the projection and contraction algorithm for solving a variational inequality in a Hilbert spac...
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In this article, we introduce an inertial projection and contraction algorithm by combining inertial type algorithms with the projection and contraction algorithm for solving a variational inequality in a Hilbert space H. In addition, we propose a modified version of our algorithm to find a common element of the set of solutions of a variational inequality and the set of fixed points of a nonexpansive mapping in H. We establish weak convergence theorems for both proposed algorithms. Finally, we give the numerical experiments to show the efficiency and advantage of the inertial projection and contraction algorithm.
In this paper, we introduce a self-adaptive inertial gradient projection algorithm for solving monotone or strongly pseudomonotone variational inequalities in real Hilbert spaces. The algorithm is designed such that t...
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In this paper, we introduce a self-adaptive inertial gradient projection algorithm for solving monotone or strongly pseudomonotone variational inequalities in real Hilbert spaces. The algorithm is designed such that the stepsizes are dynamically chosen and its convergence is guaranteed without the Lipschitz continuity and the paramonotonicity of the underlying operator. We will show that the proposed algorithm yields strong convergence without being combined with the hybrid/viscosity or linesearch methods. Our results improve and develop previously discussed gradient projection-type algorithms by Khanh and Vuong (J. Global Optim. 58, 341-350 2014).
We consider multi-group multicast beamforming in large-scale systems to minimize the transmit power subject to the signal-to-interference-plus-noise ratio (SINR) requirements. Based on the optimal multicast beamformin...
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ISBN:
(纸本)9781728176055
We consider multi-group multicast beamforming in large-scale systems to minimize the transmit power subject to the signal-to-interference-plus-noise ratio (SINR) requirements. Based on the optimal multicast beamforming structure, we propose a fast first-order algorithm to obtain the beamforming solution. The algorithm utilizes the successive convex approximation (SCA) method and solves each SCA subproblem by dual reformulation along with the extragradient method for fast closed-form updates. Initialization methods are also explored, including an extragradient-based fast initialization approach that is proposed to generate initial feasible points for SCA. Simulations show that the proposed algorithm provides a near-optimal performance with substantially lower computational complexity for large-scale systems than the existing algorithm.
In this paper we study the smooth convex-concave saddle point problem. Specifically, we analyze the last iterate convergence properties of the extragradient (EG) algorithm. It is well known that the ergodic (averaged)...
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In this paper we study the smooth convex-concave saddle point problem. Specifically, we analyze the last iterate convergence properties of the extragradient (EG) algorithm. It is well known that the ergodic (averaged) iterates of EG converge at a rate of O(1/T) (Nemirovski (2004)). In this paper, we show that the last iterate of EG converges at a rate of O(1/root T). To the best of our knowledge, this is the first paper to provide a convergence rate guarantee for the last iterate of EG for the smooth convex-concave saddle point problem. Moreover, we show that this rate is tight by proving a lower bound of Omega(1/root T) for the last iterate. This lower bound therefore shows a quadratic separation of the convergence rates of ergodic and last iterates in smooth convex-concave saddle point problems.
In this paper, we devise new iterative algorithms for solving pseudomonotone equilibrium problems in real Hilbert spaces. The advantage of our algorithms is that they require only one strongly convex programming probl...
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In this paper, we devise new iterative algorithms for solving pseudomonotone equilibrium problems in real Hilbert spaces. The advantage of our algorithms is that they require only one strongly convex programming problem at each iteration. Under suitable conditions, we establish the strong and weak convergence of the proposed algorithms. The results presented in the paper extend and improve some recent results in the literature. The performances and comparisons with some existing methods are presented through numerical examples.
In this paper, we study strongly pseudo-monotone equilibrium problems in real Hilbert and introduce two simple subgradient-type methods for solving it. The advantages of our schemes are the simplicity of their algorit...
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In this paper, we study strongly pseudo-monotone equilibrium problems in real Hilbert and introduce two simple subgradient-type methods for solving it. The advantages of our schemes are the simplicity of their algorithmic structure which consists of only one projection onto the feasible set and there is no need to solve any strongly convex programming problem, which is often used in related methods in the literature. Under mild and standard assumptions, strong convergence theorems of the proposed algorithms are established. We test and compare the performances of our schemes with some related methods in the literature for solving the Nash-Cournot oligopolistic equilibrium model.
A hybrid projection semismooth Newton algorithm (PSNA) is developed for solving two-stage stochastic variational inequalities;the algorithm is globally and superlinearly convergent under suitable assumptions. PSNA is ...
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A hybrid projection semismooth Newton algorithm (PSNA) is developed for solving two-stage stochastic variational inequalities;the algorithm is globally and superlinearly convergent under suitable assumptions. PSNA is a hybrid algorithm of the semismooth Newton algorithm and extragradient algorithm. At each step of PSNA, the second stage problem is split into a number of small variational inequality problems and solved in parallel for a fixed first stage decision iterate. The projection algorithm and semismooth Newton algorithm are used to find a new first stage decision iterate. Numerical results for large-scale nonmonotone two-stage stochastic variational inequalities and applications in traffic assignments show the efficiency of PSNA.
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