In this paper, the optimal formation and optimal matching of a multi-robot system are investigated with a projection-based algorithm designed to get the optimal formation moving in real time. The formation-related opt...
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In this paper, the optimal formation and optimal matching of a multi-robot system are investigated with a projection-based algorithm designed to get the optimal formation moving in real time. The formation-related optimization problem is proposed under the consideration of two cases: the free formation and the formation with anchor(s). For the latter, equality constraints are formulated for the anchor, and the objective of the optimal formation is to minimize the total distance to the initial formation of the multi-robot system. Here, the objective function with mixed norm is considered to get a compact formation. Sufficient conditions on the design parameter for global convergence of the proposed algorithm are provided in the theoretical results. Furthermore, the projection particle swarm optimizer is investigated for getting the optimal matching between the initial/intermediate formation and the optimal formation. Finally, simulations on several numerical examples are presented to validate the effectiveness of the proposed method.
The number of noisy images required for molecular reconstruction in single-particle cryoelectron microscopy (cryo-EM) is governed by the autocorrelations of the observed, randomly oriented, noisy projection images. In...
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The number of noisy images required for molecular reconstruction in single-particle cryoelectron microscopy (cryo-EM) is governed by the autocorrelations of the observed, randomly oriented, noisy projection images. In this work, we consider the effect of imposing sparsity priors on the molecule. We use techniques from signal processing, optimization, and applied algebraic geometry to obtain theoretical and computational contributions for this challenging nonlinear inverse problem with sparsity constraints. We prove that molecular structures modeled as sums of Gaussians are uniquely determined by the second-order autocorrelation of their projection images, implying that the sample complexity is proportional to the square of the variance of the noise. This theory improves upon the nonsparse case, where the third-order autocorrelation is required for uniformly oriented particle images and the sample complexity scales with the cube of the noise variance. Furthermore, we build a computational framework to reconstruct molecular structures which are sparse in the wavelet basis. This method combines the sparse representation for the molecule with projection-based techniques used for phase retrieval in X-ray crystallography.
This paper introduces a new version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, characterized as a scaled memoryless, projection-based, and derivative-free method for finding approximate solutions of mon...
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This paper introduces a new version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, characterized as a scaled memoryless, projection-based, and derivative-free method for finding approximate solutions of monotone nonlinear equations with convex constraints. The optimal value of the scaling parameter is achieved by minimizing the BFGS update matrix. The theoretical analysis is performed to demonstrate the global convergence of the approach. Numerical analysis and comparisons with prior results indicate that the proposed approach has superior performance for CPU time, iteration count, and function evaluations. The new algorithm is used to solve the motion control issue of a two-jointed coplanar robot manipulator.
In this study, the authors consider distributed computation of the Stein equations with set constraints, where each agent or node knows a few rows or columns of coefficient matrices. By formulating an equivalent distr...
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In this study, the authors consider distributed computation of the Stein equations with set constraints, where each agent or node knows a few rows or columns of coefficient matrices. By formulating an equivalent distributed optimisation problem, they propose a projection-based algorithm to seek least-squares solutions to the constrained Stein equation over a multi-agent system network. Then, they rigorously prove the convergence of the proposed algorithm to a least-squares solution for any initial condition, and moreover, provide a simplified distributed algorithm with an exponential convergence rate for the case without constraints.
This paper considers the constrained consensus problem over multi-cluster networks. It is assumed that the agents' states are constrained by different sets, where each constraint set is privately known by the corr...
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This paper considers the constrained consensus problem over multi-cluster networks. It is assumed that the agents' states are constrained by different sets, where each constraint set is privately known by the corresponding agent. Within this framework, a hierarchical projection-based consensus algorithm is presented to solve the considered problem. Technically, the consensus analysis of the proposed algorithm consists of the following three aspects: First, by using the property of the projection operator, the limiting behaviors of the agents' states generated by the algorithm are investigated. Then, based on the limiting behaviors, it is proven that the agents' states in the whole network achieve a constrained consensus. Furthermore, by introducing an important auxiliary variable that relates to the agents' states, the linear convergence of the proposed algorithm is proved. Compared with the existing results, this paper generalizes the constrained consensus methods under single-cluster networks to the multi-cluster ones. Finally, simulations are given to verify the theoretical results. (C) 2018 Elsevier Inc. All rights reserved.
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