Motivated by the convergence result of mirror-descent algorithms to market equilibria in linear Fisher markets, it is natural for one to consider designing dynamics (specifically, iterative algorithms) for agents to a...
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Motivated by the convergence result of mirror-descent algorithms to market equilibria in linear Fisher markets, it is natural for one to consider designing dynamics (specifically, iterative algorithms) for agents to arrive at linear Arrow-Debreu market equilibria. Jain (SIAM J. Comput. 37(1), 303-318,2007) reduced equilibrium computation in linear Arrow-Debreu markets to the equilibrium computation in bijective markets, where everyone is a seller of only one good and a buyer for a bundle of goods. In this paper, we design an algorithm for computing linear bijective market equilibrium, based on solving the rational convex program formulated by Devanur et al. The algorithm repeatedly alternates between a step of gradient-descent-like updates and a distributed step of optimization exploiting the property of such convex program. Convergence can be ensured by a new analysis different from the analysis for linear Fisher market equilibria.
Let X be a uniformly convex and uniformly smooth Banach space. Assume that the M-i, i = 1,..., r, are closed linear subspaces of X, P-Mi is the best approximation operator to the linear subspace M-i and M := M-1 +...+...
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Let X be a uniformly convex and uniformly smooth Banach space. Assume that the M-i, i = 1,..., r, are closed linear subspaces of X, P-Mi is the best approximation operator to the linear subspace M-i and M := M-1 +...+ M-r. We prove that if M is closed, then the alternating algorithm given by repeated iterations of (I - P-Mr) (I - PMr-1) ... (I - P-M1) applied to any x is an element of X converges to x - P(M)x is the best approximation Operator to the linear subspace M. This result, in the case r = 2, was proven in Deutsch [4]. (C) 2014 Elsevier Inc. All rights reserved.
Given two nonempty and disjoint intersections of closed and convex subsets, we look for a best approximation pair relative to them, i.e., a pair of points, one in each intersection, attaining the minimum distance betw...
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Given two nonempty and disjoint intersections of closed and convex subsets, we look for a best approximation pair relative to them, i.e., a pair of points, one in each intersection, attaining the minimum distance between the disjoint intersections. We propose an iterative process based on projections onto the subsets which generate the intersections. The process is inspired by the Halpern-Lions-Wittmann- Bauschke algorithm and the classical alternating process of Cheney and Goldstein, and its advantage is that there is no need to project onto the intersections themselves, a task which can be rather demanding. We prove that under certain conditions the two interlaced subsequences converge to a best approximation pair. These conditions hold, in particular, when the space is Euclidean and the subsets which generate the intersections are compact and strictly convex. Our result extends the one of Aharoni, Censor and Jiang ["Finding a best approximation pair of points for two polyhedra", Computational Optimization and Applications 71 (2018), 509-23] who considered the case of finite-dimensional polyhedra.
The cooling process of hot-rolled coil directly affects the mechanical and metallurgical properties of the final product. The non -uniform behavior of temperature and microstructure can easily result in sufficient res...
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The cooling process of hot-rolled coil directly affects the mechanical and metallurgical properties of the final product. The non -uniform behavior of temperature and microstructure can easily result in sufficient residual stress to induce subsequent cutting deformation. Therefore, the focus of this study is to analyze the thermalmetallurgical coupling problem during the cooling process of hot-rolled coil. Unlike before, a symplectic analytical approach is proposed to calculate the temperature and microstructure evolution of hot-rolled coil. Firstly, the hot-rolled coil is discretized to convert the three-dimensional heat transfer problem in cylindrical coordinate system to cartesian coordinate system. Then, the traditional heat transfer model is introduced into the symplectic Hamiltonian system and the symplectic superposition method is employed to handle complex cooling boundary conditions. The symplectic analytical solution of the three-dimensional temperature field is obtained through rigorous derivation without any assumptions or predetermined solution forms. Meanwhile, an alternating algorithm is designed between the heat transfer model and the phase transformation dynamics model to realize the coupling process. Moreover, a high-precision finite element model verified by the measured data is established. The symplectic analytical solution of coil temperature and microstructure during the cooling process is in good agreement with the finite element solution. Finally, the symplectic approach has been proven to enable quantitative mathematical analysis of the coupling mechanism of thermal-metallurgical processes.
Recent years have witnessed a surge in demand for air cargo transportation. Air cargo terminals initially built for handling the former demand volume start struggling with low operational efficiency and high congestio...
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Recent years have witnessed a surge in demand for air cargo transportation. Air cargo terminals initially built for handling the former demand volume start struggling with low operational efficiency and high congestion due to limited capacity. The industry has explored methods such as building new terminals and renting warehouses to stay competitive in the market. However, these methods may not be practical in many scenarios due to economic reasons and the scarcity of airport land. As an alternative method, this paper investigates an innovative operational paradigm with the concept of Offshore Consolidation Centre (OCC) to deal with the imbalance between the surging demand and the limited capacity of air cargo terminals. We redesign air cargo terminal operations with the existence of OCC and formulate the problem as a mixed-integer linear program (MILP). We then propose a two-stage alternating algorithm embedded with a tailored metaheuristic to analyse the validity of our model and algorithm. Experiment results reveal that our alternating algorithm has the best performance compared with the solver and benchmark policies adopted in industrial practice. Moreover, the comparison with air cargo terminals without OCC demonstrates that OCC can reduce delays, cargo waiting time, and traffic flow, by a large margin.
We formulate the manifold learning problem as the problem of finding an operator that maps any point to a close neighbor that lies on a "hidden" k-dimensional manifold. We call this operator the correcting f...
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We formulate the manifold learning problem as the problem of finding an operator that maps any point to a close neighbor that lies on a "hidden" k-dimensional manifold. We call this operator the correcting function. Under this formulation, autoencoders can be viewed as a tool to approximate the correcting function. Given an autoencoder whose Jacobian has rank k , we deduce from the classical Constant Rank Theorem that its range has a structure of a k-dimensional manifold. A k-dimensionality of the range can be forced by the architecture of an autoencoder (by fixing the dimension of the code space), or alternatively, by an additional constraint that the rank of the autoencoder mapping is not greater than k . This constraint is included in the objective function as a new term, namely a squared Ky-Fan k-antinorm of the Jacobian function. We claim that this constraint is a factor that effectively reduces the dimension of the range of an autoencoder, additionally to the reduction defined by the architecture. We also add a new curvature term into the objective. To conclude, we experimentally compare our approach with the CAE+H method on synthetic and real-world datasets.& COPY;2023 Elsevier Ltd. All rights reserved.
Let H-1, H-2 H-3 be real Hilbert spaces, let C subset of H-1, Q subset of H-2 be two nonempty closed convex level sets, let A : H-1 -> H-3, B : H-2 -> H-3 be two bounded linear operators. Our interest is in solv...
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Let H-1, H-2 H-3 be real Hilbert spaces, let C subset of H-1, Q subset of H-2 be two nonempty closed convex level sets, let A : H-1 -> H-3, B : H-2 -> H-3 be two bounded linear operators. Our interest is in solving the following new convex feasibility problem Find x is an element of C, y is an element of Q such that Ax = By, (1.1) which allows asymmetric and partial relations between the variables x and y. In this paper, we present and study the convergence of a relaxed alternating CQ-algorithm (RACQA) and show that the sequences generated by such an algorithm weakly converge to a solution of (1.1). The interest of RACQA is that we just need projections onto half-spaces, thus making the relaxed CQ-algorithm implementable. Note that, by taking B = I, in (1.1), we recover the split convex feasibility problem originally introduced in Censor and Elfving (1994) [13] and used later in intensity-modulated radiation therapy (Censor et al. (2006) [11]). We also recover the relaxed CQ-algorithm introduced by Yang (2004) [8] by particularizing both B and a given parameter. (C) 2012 Elsevier Ltd. All rights reserved.
Future wireless technologies, such as fifth-generation (5G), are expected to support real-time applications with high data throughput, e.g., holographic meetings. From a bandwidth perspective, cognitive radio (CR) is ...
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Future wireless technologies, such as fifth-generation (5G), are expected to support real-time applications with high data throughput, e.g., holographic meetings. From a bandwidth perspective, cognitive radio (CR) is a promising technology to enhance the system's throughput via sharing the licensed spectrum. From a delay perspective, it is well known that increasing the number of decoding blocks will improve system robustness against errors while increasing delay. Therefore, optimally allocating the resources to determine the tradeoff of tuning the length of the decoding blocks while sharing the spectrum is a critical challenge for future wireless systems. In this paper, we minimize the targeted outage probability over the block-fading channels while utilizing the spectrum-sharing concept. The secondary user's outage region and the corresponding optimal power are derived, over two-block and M-block fading channels. We propose two suboptimal power strategies and derive the associated asymptotic lower and upper bounds on the outage probability with tractable expressions. These bounds allow us to derive the exact diversity order of the secondary user's outage probability. To further enhance the system's performance, we also investigate the impact of including the sensing information on the outage problem. The outage problem is then solved via proposing an alternating optimization algorithm, which utilizes the verified strict quasi-convex structure of the problem. Selected numerical results are presented to characterize the system's behavior and show the improvements of several sharing concepts.
This paper studies the problem of split convex feasibility and a strong convergent alternating algorithm is *** to this algorithm,some strong convergent theorems are obtained and an affirmative answer to the question ...
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This paper studies the problem of split convex feasibility and a strong convergent alternating algorithm is *** to this algorithm,some strong convergent theorems are obtained and an affirmative answer to the question raised by Moudafi is *** the same time,this paper also generalizes the problem of split convex feasibility.
This paper proposes an alternating optimization algorithm for addressing the secrecy rate optimization problem for a multi-input-multi-output (MIMO) secrecy channel in the presence of a multiantenna eavesdropper, wher...
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ISBN:
(纸本)9781479980888
This paper proposes an alternating optimization algorithm for addressing the secrecy rate optimization problem for a multi-input-multi-output (MIMO) secrecy channel in the presence of a multiantenna eavesdropper, where a multiantenna cooperative jammer will be employed to confuse the eavesdropper by introducing jamming signal. We investigate the secrecy rate maximization problem, which is a non-convex problem in terms of transmit covariance matrices of the legitimate transmitter and the cooperative jammer. In order to circumvent this issue, we develop an optimization algorithm by alternating optimizing the transmit covariance matrices of the legitimate transmitter and the cooperative jammer where each transmit covariance matrix is optimized while other is fixed. Based on this algorithm, we develop a robust scheme by incorporating channel uncertainties associated with the eavesdropper. By exploiting S-Procedure, we show that these robust optimization problems can be formulated into semidefinite programming (SDP). Simulation results have been provided to validate the convergence and the performance of the alternating algorithm.
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