Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are bu...
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Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear compositions, and infimal convolutions of simple functions so that each simple term is processed individually via proximal mappings, gradient mappings, and multiplications by the linear maps. This leads to easily implementable and highly parallelizable or distributed algorithms, which often obtain nearly state-of-the-art performance. In this paper, we analyze a monotone inclusion problem that captures a large class of primal-dual splittings as a special case. We introduce a unifying scheme and use some abstract analysis of the algorithm to prove convergence rates of the proximal pointalgorithm, forward-backward splitting, Peaceman-Rachford splitting, and forward-backward-forward splitting applied to the model problem. Our ergodic convergence rates are deduced under variable metrics, stepsizes, and relaxation parameters. Our nonergodic convergence rates are the first shown in the literature. Finally, we apply our results to a large class of primal-dual algorithms that are a special case of our scheme and deduce their convergence rates.
Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixedpointalgorithms in Hilbert spaces. An extended version of the forward back...
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Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixedpointalgorithms in Hilbert spaces. An extended version of the forward backward splitting algorithm for finding a zero of the sum of two monotone operators is obtained. (C) 2014 Elsevier Inc. All rights reserved.
We consider a class of complementarity problems involving functions which are nonlinear. In this paper we reformulate this nonlinear complementarity problem as a system of absolute value equations (which is nonsmooth)...
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We consider a class of complementarity problems involving functions which are nonlinear. In this paper we reformulate this nonlinear complementarity problem as a system of absolute value equations (which is nonsmooth). Then we propose a fixed-point method to solve this nonsmooth system. We prove that the proposed method is globally linearly convergent under a mild condition. The proposed method is greatly effective not only for small and medium size problems, but also for large and super-large scale problems. Especially, our method can efficiently solve super-large scale problems, with a million variables, in a few tens of minutes on a PC. (C) 2014 Elsevier Ltd. All rights reserved.
Classical independent component analysis (ICA) has been reasonably successful;however, the performance and the convergence of the conventional ICA algorithms have reached limitations of further improvement since they ...
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Classical independent component analysis (ICA) has been reasonably successful;however, the performance and the convergence of the conventional ICA algorithms have reached limitations of further improvement since they utilize only the statistical independency among the sources. For circumventing this situation, in this paper, we incorporate some other kinds of temporal priori information, i.e., the generalized autocorrelation and the nonlinear predictability of each source, and make a convex combination of them to formulate a novel cost function for blind source separation (BSS). With this cost function, a fixed-point BSS algorithm is developed. This algorithm inherits the advantages of the well-known FastICA algorithm of ICA, which converges fast and does not need to choose any learning step sizes. Its higher separation accuracy is verified by numerical experiments. Meanwhile, we also give the consistency analysis and prove convergence properties of the algorithm, which has a (locally) consistent estimator and at least quadratic convergence. (C) 2014 Elsevier B.V. All rights reserved.
A simple, inexpensive and sensitive kinetic spectrophotometric method was developed for the simultaneous determination of three anti-carcinogenic flavonoids: catechin, quercetin and naringenin, in fruit samples. A yel...
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A simple, inexpensive and sensitive kinetic spectrophotometric method was developed for the simultaneous determination of three anti-carcinogenic flavonoids: catechin, quercetin and naringenin, in fruit samples. A yellow chelate product was produced in the presence neocuproine and Cu(I) - a reduction product of the reaction between the flavonoids with Cu(II), and this enabled the quantitative measurements with UV-vis spectrophotometry. The overlapping spectra obtained, were resolved with chemometrics calibration models, and the best performing method was the fast independent component analysis (fast-ICA/PCR (Principal component regression));the limits of detection were 0.075, 0.057 and 0.063 mg L-1 for catechin, quercetin and naringenin, respectively. The novel method was found to outperform significantly the common HPLC procedure. (C) 2013 Elsevier B.V. All rights reserved.
This paper addresses blind source separation (BSS) problem when source signals have the temporal structure with nonlinear autocorrelation. Using the temporal characteristics of sources, we develop an objective functio...
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This paper addresses blind source separation (BSS) problem when source signals have the temporal structure with nonlinear autocorrelation. Using the temporal characteristics of sources, we develop an objective function based on the nonlinear autocorrelation of sources. Maximizing the objective function, we propose a fixed-point source separation algorithm. Furthermore, we give some mathematical properties of the algorithm. Computer simulations for sources with square temporal autocorrelation and the real-world applications in the analysis of the magnetoencephalographic recordings (MEG) illustrate the efficiency of the proposed approach. Thus, the presented BSS algorithm, which is based on the nonlinear measure of temporal autocorrelation, provides a novel statistical property to perform BSS. (C) 2008 Elsevier B.V. All rights reserved.
This paper introduces a highly efficient waterfilling-based strategy for optimal use of the channel in vehicular or personal ad-hoc communications. The approach provides near optimum allocation of resources and enable...
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ISBN:
(纸本)9781467362337
This paper introduces a highly efficient waterfilling-based strategy for optimal use of the channel in vehicular or personal ad-hoc communications. The approach provides near optimum allocation of resources and enables small communications devices to establish connections when the energy efficiency is at its best. Instead of calculating the transmit power through conventional waterfilling, the proposed algorithm calculates the waterlevel, thus providing a decision threshold and a strategy for optimum use of the time-variant channel at the same time. The algorithm adapts to the changing average channel quality by applying an exponentially-weighted moving-average (EWMA) trigger to re-calculate the waterlevel. The new algorithm is compared to an efficient non-iterative algorithm that directly calculates the transmit powers in every time-slot. It is shown that the new strategy reduces computation time by approximately 90% compared to the classic approach without compromising performance measures such as transmitted information or energy. Practical implementation is briefly discussed to demonstrate suitability of the algorithm for integration into tomorrow's communication devices.
Independent component analysis (ICA) aims to recover a set of unknown mutually independent components (ICs) from their observed mixtures without knowledge of the mixing coefficients. In the classical ICA model there e...
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Independent component analysis (ICA) aims to recover a set of unknown mutually independent components (ICs) from their observed mixtures without knowledge of the mixing coefficients. In the classical ICA model there exists ICs' indeterminacy on permutation and dilation. Constrained ICA is one of methods for solving this problem through introducing constraints into the classical ICA model. In this paper we first present a new constrained ICA model which composed of three pans: a maximum likelihood criterion as an objective function, statistical measures as inequality constraints and the normalization of demixing matrix as equality constraints. Next, we incorporate the new fixed-point (newFP) algorithm into this constrained ICA model to construct a new constrained fixed-point algorithm. Computation simulations on synthesized signals and speech signals demonstrate that this combination both can eliminate ICs' indeterminacy to a certain extent, and can provide better performance. Moreover, comparison results with the existing algorithm verify the efficiency of our new algorithm furthermore, and show that it is more simple to implement than the existing algorithm due to its advantage of not using the learning rate. Finally. this new algorithm is also applied for the real-world fetal ECG data. experiment results further indicate the efficiency of the new constrained fixed-point algorithm. (c) 2007 Published by Elsevier B.V.
This paper introduces a highly efficient waterfilling-based strategy for optimal use of the channel in vehicular or personal ad-hoc communications. The approach provides near optimum allocation of resources and enable...
详细信息
ISBN:
(纸本)9781467362337
This paper introduces a highly efficient waterfilling-based strategy for optimal use of the channel in vehicular or personal ad-hoc communications. The approach provides near optimum allocation of resources and enables small communications devices to establish connections when the energy efficiency is at its best. Instead of calculating the transmit power through conventional waterfilling, the proposed algorithm calculates the waterlevel, thus providing a decision threshold and a strategy for optimum use of the time-variant channel at the same time. The algorithm adapts to the changing average channel quality by applying an exponentially-weighted moving-average (EWMA) trigger to re-calculate the waterlevel. The new algorithm is compared to an efficient non-iterative algorithm that directly calculates the transmit powers in every time-slot. It is shown that the new strategy reduces computation time by approximately 90% compared to the classic approach without compromising performance measures such as transmitted information or energy. Practical implementation is briefly discussed to demonstrate suitability of the algorithm for integration into tomorrow's communication devices.
When auxiliary information is available at the design stage, samples may be selected by means of balanced sampling. The variance of the Horvitz-Thompson estimator is then reduced, since it is approximately given by th...
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When auxiliary information is available at the design stage, samples may be selected by means of balanced sampling. The variance of the Horvitz-Thompson estimator is then reduced, since it is approximately given by that of the residuals of the variable of interest on the balancing variables. In this paper, a method for computing optimal inclusion probabilities for balanced sampling on given auxiliary variables is studied. We show that the method formerly suggested by Title and Favre (2005) enables the computation of inclusion probabilities that lead to a decrease in variance under some conditions on the set of balancing variables. A disadvantage is that the target optimal inclusion probabilities depend on the variable of interest. If the needed quantities are unknown at the design stage, we propose to use estimates instead (e.g., arising from a previous wave of the survey). A limited simulation study suggests that, under some conditions, our method performs better than the method of Title and Favre (2005). (C) 2010 Elsevier B.V. All rights reserved.
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