The Experts below are selected from a list of 1226196 Experts worldwide ranked by ideXlab platform
Jun Wang - One of the best experts on this subject based on the ideXlab platform.
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Primal and dual neural networks for shortest-path routing
IEEE Transactions on Systems Man and Cybernetics - Part A: Systems and Humans, 1998Co-Authors: Jun WangAbstract:Presents two recurrent neural networks for solving the shortest path problem. Simplifying the architecture of a recurrent neural network based on the primal problem formulation, the first recurrent neural network called the primal routing network has less complex connectivity than its predecessor. Based on the dual problem formulation, the second recurrent neural network called the dual routing network has even simpler architecture. While being simple in architecture, the primal and dual routing networks are capable of shortest-path routing like their predecessor.
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Analysis and design of Primal-Dual assignment networks
IEEE transactions on neural networks, 1998Co-Authors: Jun Wang, Youshen XiaAbstract:The assignment problem is an archetypical combinatorial optimization problem having widespread applications. This paper presents two recurrent neural networks, a continuous-time one and a discrete-time one, for solving the assignment problem. Because the proposed recurrent neural networks solve the primal and dual assignment problems simultaneously, they are called Primal-Dual assignment networks. The Primal-Dual assignment networks are guaranteed to make optimal assignment regardless of initial conditions. Unlike the primal or dual assignment network, there is no time-varying design parameter in the Primal-Dual assignment networks. Therefore, they are more suitable for hardware implementation. The performance and operating characteristics of the Primal-Dual assignment networks are demonstrated by means of illustrative examples.
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A discrete-time Primal-Dual assignment network
1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227), 1Co-Authors: Jun Wang, Youshen XiaAbstract:Presents a discrete-time recurrent neural network for solving the assignment problem. Because the proposed recurrent neural network solves the primal and dual assignment problems simultaneously, it is called the Primal-Dual assignment network. The Primal-Dual assignment network is guaranteed to make optimal assignment regardless of initial conditions. Unlike the primal or dual assignment network, there is no time-varying design parameter in the Primal-Dual assignment network. Therefore, it is more suitable for hardware implementation. The performance and operating characteristics of the Primal-Dual assignment network are demonstrated by means of illustrative examples.
Youshen Xia - One of the best experts on this subject based on the ideXlab platform.
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Analysis and design of Primal-Dual assignment networks
IEEE transactions on neural networks, 1998Co-Authors: Jun Wang, Youshen XiaAbstract:The assignment problem is an archetypical combinatorial optimization problem having widespread applications. This paper presents two recurrent neural networks, a continuous-time one and a discrete-time one, for solving the assignment problem. Because the proposed recurrent neural networks solve the primal and dual assignment problems simultaneously, they are called Primal-Dual assignment networks. The Primal-Dual assignment networks are guaranteed to make optimal assignment regardless of initial conditions. Unlike the primal or dual assignment network, there is no time-varying design parameter in the Primal-Dual assignment networks. Therefore, they are more suitable for hardware implementation. The performance and operating characteristics of the Primal-Dual assignment networks are demonstrated by means of illustrative examples.
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A discrete-time Primal-Dual assignment network
1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227), 1Co-Authors: Jun Wang, Youshen XiaAbstract:Presents a discrete-time recurrent neural network for solving the assignment problem. Because the proposed recurrent neural network solves the primal and dual assignment problems simultaneously, it is called the Primal-Dual assignment network. The Primal-Dual assignment network is guaranteed to make optimal assignment regardless of initial conditions. Unlike the primal or dual assignment network, there is no time-varying design parameter in the Primal-Dual assignment network. Therefore, it is more suitable for hardware implementation. The performance and operating characteristics of the Primal-Dual assignment network are demonstrated by means of illustrative examples.
Lieven Vandenberghe - One of the best experts on this subject based on the ideXlab platform.
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primal dual decomposition by operator splitting and applications to image deblurring
Siam Journal on Imaging Sciences, 2014Co-Authors: Daniel T Oconnor, Lieven VandenbergheAbstract:We present Primal-Dual decomposition algorithms for convex optimization problems with cost functions $f(x)+g(Ax)$, where $f$ and $g$ have inexpensive proximal operators and $A$ can be decomposed as a sum of two structured matrices. The methods are based on the Douglas--Rachford splitting algorithm applied to various splittings of the Primal-Dual optimality conditions. We discuss applications to image deblurring problems with nonquadratic data fidelity terms, different types of convex regularization, and simple convex constraints. In these applications, the Primal-Dual splitting approach allows us to handle general boundary conditions for the blurring operator. Numerical results indicate that the Primal-Dual splitting methods compare favorably with the alternating direction method of multipliers, the Douglas--Rachford algorithm applied to a reformulated primal problem, and the Chambolle--Pock Primal-Dual algorithm.
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Primal-Dual Decomposition by Operator Splitting and Applications to Image Deblurring ∗
SIAM Journal on Imaging Sciences, 2014Co-Authors: Daniel T. O'connor, Lieven VandenbergheAbstract:We present Primal-Dual decomposition algorithms for convex optimization problems with cost functions $f(x)+g(Ax)$, where $f$ and $g$ have inexpensive proximal operators and $A$ can be decomposed as a sum of two structured matrices. The methods are based on the Douglas--Rachford splitting algorithm applied to various splittings of the Primal-Dual optimality conditions. We discuss applications to image deblurring problems with nonquadratic data fidelity terms, different types of convex regularization, and simple convex constraints. In these applications, the Primal-Dual splitting approach allows us to handle general boundary conditions for the blurring operator. Numerical results indicate that the Primal-Dual splitting methods compare favorably with the alternating direction method of multipliers, the Douglas--Rachford algorithm applied to a reformulated primal problem, and the Chambolle--Pock Primal-Dual algorithm.
Robert Kleinberg - One of the best experts on this subject based on the ideXlab platform.
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randomized primal dual analysis of ranking for online bipartite matching
Symposium on Discrete Algorithms, 2013Co-Authors: Nikhil R Devanur, Kamal Jain, Robert KleinbergAbstract:We give a simple proof that the ranking algorithm of Karp, Vazirani and Vazirani [KVV90] is 1-1/e competitive for the online bipartite matching problem. The proof is via a randomized Primal-Dual argument. Primal-Dual algorithms have been successfully used for many online algorithm problems, but the dual constraints are always satisfied deterministically. This is the first instance of a non-trivial randomized Primal-Dual algorithm in which the dual constraints only hold in expectation. The approach also generalizes easily to the vertex-weighted version considered by Agarwal et al. [AGKM11]. Further we show that the proof is very similar to the deterministic Primal-Dual argument for the online budgeted allocation problem with small bids (also called the AdWords problem) of Mehta et al. [MSVV05].
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SODA - Randomized Primal-Dual analysis of RANKING for online bipartite matching
2013Co-Authors: Nikhil R Devanur, Kamal Jain, Robert KleinbergAbstract:We give a simple proof that the ranking algorithm of Karp, Vazirani and Vazirani [KVV90] is 1-1/e competitive for the online bipartite matching problem. The proof is via a randomized Primal-Dual argument. Primal-Dual algorithms have been successfully used for many online algorithm problems, but the dual constraints are always satisfied deterministically. This is the first instance of a non-trivial randomized Primal-Dual algorithm in which the dual constraints only hold in expectation. The approach also generalizes easily to the vertex-weighted version considered by Agarwal et al. [AGKM11]. Further we show that the proof is very similar to the deterministic Primal-Dual argument for the online budgeted allocation problem with small bids (also called the AdWords problem) of Mehta et al. [MSVV05].
Jorge Cortes - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic convergence of constrained primal–dual dynamics
Systems & Control Letters, 2016Co-Authors: Ashish Cherukuri, Enrique Mallada, Jorge CortesAbstract:This paper studies the asymptotic convergence properties of the primal–dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the primal–dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the primal–dual optimizers are globally asymptotically stable under the primal–dual dynamics and that each solution of the dynamics converges to an optimizer.
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Asymptotic convergence of constrained Primal-Dual dynamics
arXiv: Optimization and Control, 2015Co-Authors: Ashish Cherukuri, Enrique Mallada, Jorge CortesAbstract:This paper studies the asymptotic convergence properties of the Primal-Dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the Primal-Dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the Primal-Dual optimizers are globally asymptotically stable under the Primal-Dual dynamics and that each solution of the dynamics converges to an optimizer.
