The affine rank minimization problem is to minimize the rank of a matrix under linear constraints. It has many applications in various areas such as statistics, control, system identification and machine learning. Unl...
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The affine rank minimization problem is to minimize the rank of a matrix under linear constraints. It has many applications in various areas such as statistics, control, system identification and machine learning. Unlike the literatures which use the nuclear norm or the general Schatten quasi-norm to approximate the rank of a matrix, in this paper we use the Schatten 1 / 2 quasi-norm approximation which is a better approximation than the nuclear norm but leads to a nonconvex, nonsmooth and non-Lipschitz optimization problem. It is important that we give a global necessary optimality condition for the regularization problem by virtue of the special objective function. This is very different from the local optimality conditions usually used for the general regularization problems. Explicitly, the global necessary optimality condition for the regularization problem is a fixedpoint inclusion associated with the singular value half thresholding operator. Naturally, we propose a fixedpoint iterative scheme for the problem. We also provide the convergence analysis of this iteration. By discussing the location and setting of the optimal regularization parameter as well as using an approximate singular value decomposition procedure, we get a very efficient algorithm, half norm fixed point algorithm with an approximate SVD (HFPA algorithm), for the regularization problem. Numerical experiments on randomly generated and real matrix completion problems are presented to demonstrate the effectiveness of the proposed algorithm.
This paper introduces an elliptic quasi-variational inequality (QVI) problem class with fractional diffusion of order s is an element of (0, 1), studies existence and uniqueness of solutions and develops a solution al...
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This paper introduces an elliptic quasi-variational inequality (QVI) problem class with fractional diffusion of order s is an element of (0, 1), studies existence and uniqueness of solutions and develops a solution algorithm. As the fractional diffusion prohibits the use of standard tools to approximate the QVI, instead we realize it as a Dirichlet-to-Neumann map for a problem posed on a semi-infinite cylinder. We first study existence and uniqueness of solutions for this extended QVI and then transfer the results to the fractional QVI: This introduces a new paradigm in the field of fractional QVIs. Further, we truncate the semi-infinite cylinder and show that the solution to the truncated problem converges to the solution of the extended problem, under fairly mild assumptions, as the truncation parameter r tends to infinity. Since the constraint set changes with the solution, we develop an argument using Mosco convergence. We state an algorithm to solve the truncated problem and show its convergence in function space. Finally, we conclude with several illustrative numerical examples.
Maximum correntropy criteria (MCC) has been exhibited a robustness against impulse noise by applying various area of signal process. MCC has been shown to be a rather robust adaption principle for adaptive system trai...
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ISBN:
(纸本)9781509012855
Maximum correntropy criteria (MCC) has been exhibited a robustness against impulse noise by applying various area of signal process. MCC has been shown to be a rather robust adaption principle for adaptive system training in the presence of heavy-tailed non Gaussian noises. fixed point algorithms converge to the optimum solution more quickly for fixed signals. In this paper shows convergence of a Dynamic Harmonic Balance algorithms with sufficient condition and comparison between fixed point algorithm and Dynamic Harmonic Balance algorithm.
Maximum correntropy criteria (MCC) has been exhibited a robustness against impulse noise by applying various area of signal process. MCC has been shown to be a rather robust adaption principle for adaptive system trai...
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ISBN:
(纸本)9781509012862
Maximum correntropy criteria (MCC) has been exhibited a robustness against impulse noise by applying various area of signal process. MCC has been shown to be a rather robust adaption principle for adaptive system training in the presence of heavy-tailed non Gaussian noises. fixed point algorithms converge to the optimum solution more quickly for fixed signals. In this paper shows convergence of a Dynamic Harmonic Balance algorithms with sufficient condition and comparison between fixed point algorithm and Dynamic Harmonic Balance algorithm.
In this paper, we consider the problem of blind identification in the underdetermined instantaneous mixtures case, where there are more sources than sensors. Recently, a simultaneous matrix diagonalization (SMD)-based...
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ISBN:
(纸本)9781424451821
In this paper, we consider the problem of blind identification in the underdetermined instantaneous mixtures case, where there are more sources than sensors. Recently, a simultaneous matrix diagonalization (SMD)-based method has been proposed without any need of sparsity assumption on sources. Instead of using SMD technique, we propose a fixed point algorithm, which estimates the columns of the mixing matrix sequentially one by one. Computer simulations are presented in order to demonstrate that the proposed algorithm has the ability to identify the mixing matrix, and its performance is comparable to that of SMD-based algorithm.
An optimality criteria (OC)-based algorithm for optimization of a general class of nonlinear programming (NLP) problems is presented. The algorithm is only applicable to problems where the objective and constraint fun...
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An optimality criteria (OC)-based algorithm for optimization of a general class of nonlinear programming (NLP) problems is presented. The algorithm is only applicable to problems where the objective and constraint functions satisfy certain monotonicity properties. For multiply constrained problems which satisfy these assumptions, the algorithm is attractive compared with existing NLP methods as well as prevalent OC methods, as the latter involve computationally expensive active set and step-size control strategies. The fixed point algorithm presented here is applicable not only to structural optimization problems but also to certain problems as occur in resource allocation and inventory models. Convergence aspects are discussed. The fixedpoint update or resizing formula is given physical significance, which brings out a strength and trim feature. The number of function evaluations remains independent of the number of variables, allowing the efficient solution of problems with large number of variables.
We present a novel approach to detect the trajectories of particles by combining (a) adaptive dictionaries that model physically consistent spatio-temporal events, and (b) convex programming for sparse matching and tr...
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ISBN:
(纸本)9783319146126;9783319146119
We present a novel approach to detect the trajectories of particles by combining (a) adaptive dictionaries that model physically consistent spatio-temporal events, and (b) convex programming for sparse matching and trajectory detection in image sequence data. The mutual parametrization of these two components are mathematically designed so as to achieve provable convergence of the overall scheme to a fixedpoint. While this work is motivated by the task of estimating instantaneous vessel blood flow velocity using ultrasound image velocimetry, our contribution from the optimization point of view may be of interest also to related pattern and image analysis tasks in different application fields.
An optimality criteria (OC)-based algorithm for optimization of a general class of nonlinear programming (NLP) problems is presented. The algorithm is only applicable to problems where the objective and constraint fun...
详细信息
An optimality criteria (OC)-based algorithm for optimization of a general class of nonlinear programming (NLP) problems is presented. The algorithm is only applicable to problems where the objective and constraint functions satisfy certain monotonicity properties. For multiply constrained problems which satisfy these assumptions, the algorithm is attractive compared with existing NLP methods as well as prevalent OC methods, as the latter involve computationally expensive active set and step-size control strategies. The fixed point algorithm presented here is applicable not only to structural optimization problems but also to certain problems as occur in resource allocation and inventory models. Convergence aspects are discussed. The fixedpoint update or resizing formula is given physical significance, which brings out a strength and trim feature. The number of function evaluations remains independent of the number of variables, allowing the efficient solution of problems with large number of variables.
In this paper, we consider the problem of blind identification in the underdetermined instantaneous mixtures case, where there are more sources than sensors. Recently, a simultaneous matrix diagonalization (SMD)-based...
详细信息
In this paper, we consider the problem of blind identification in the underdetermined instantaneous mixtures case, where there are more sources than sensors. Recently, a simultaneous matrix diagonalization (SMD)-based method has been proposed without any need of sparsity assumption on sources. Instead of using SMD technique, we propose a fixed point algorithm, which estimates the columns of the mixing matrix sequentially one by one. Computer simulations are presented in order to demonstrate that the proposed algorithm has the ability to identify the mixing matrix, and its performance is comparable to that of SMD-based algorithm.
In this paper,we consider the problem of blind identification in the underdetermined instantaneous mixtures case,where there are more sources than ***,a simultaneous matrix diagonalization(SMD)-based method has been p...
详细信息
In this paper,we consider the problem of blind identification in the underdetermined instantaneous mixtures case,where there are more sources than ***,a simultaneous matrix diagonalization(SMD)-based method has been proposed without any need of sparsity assumption on *** of using SMD technique,we propose a fixed point algorithm,which estimates the columns of the mixing matrix sequentially one by *** simulations are presented in order to demonstrate that the proposed algorithm has the ability to identify the mixing matrix,and its performance is comparable to that of SMD-based algorithm.
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