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921.
In this paper, we give a lower bound guaranteeing exact matrix completion via singular value thresholding (SVT) algorithm. The analysis shows that when the parameter in SVT algorithm is beyond some finite scalar, one can recover some unknown low-rank matrices exactly with high probability by solving a strictly convex optimization problem. Furthermore, we give an explicit expression for such a finite scalar. This result in the paper not only has theoretical interests, but also guides us to choose suitable parameters in the SVT algorithm. 相似文献
922.
Haowei Zhang Junwei Xie Jiaang Ge Zhaojian Zhang Binfeng Zong 《European Journal of Operational Research》2019,272(3):868-878
A phased array radar (PAR) is used to detect new targets and update the information of those detected targets. Generally, a large number of tasks need to be performed by a single PAR in a finite time horizon. In order to utilize the limited time and the energy resources, it is necessary to provide an efficient task scheduling algorithm. However, the existing radar task scheduling algorithms can't be utilized to release the full potential of the PAR, because of those disadvantages such as full PAR task structure ignored, only good performance in one aspect considered and just heuristic or the meta-heuristic method utilized. Aiming at above issues, an optimization model for the PAR task scheduling and a hybrid adaptively genetic (HAGA) algorithm are proposed. The model considers the full PAR task structure and integrates multiple principles of task scheduling, so that multi-aspect performance can be guaranteed. The HAGA incorporates the improved GA to explore better solutions while using the heuristic task interleaving algorithm to utilize wait intervals to interleave subtasks and calculate fitness values of individuals in efficient manners. Furthermore, the efficiency and the effectiveness of the HAGA are both improved by adopting chaotic sequences for the population initialization, the elite reservation and the mixed ranking selection, as well as designing the adaptive crossover and the adaptive mutation operators. The simulation results demonstrate that the HAGA possesses merits of global exploration, faster convergence, and robustness compared with three state-of-art algorithms—adaptive GA, hybrid GA and highest priority and earliest deadline first heuristic (HPEDF) algorithm. 相似文献
923.
Customized personal rate offering is of growing importance in the insurance industry. To achieve this, an important step is to identify subgroups of insureds from the corresponding heterogeneous claim frequency data. In this paper, a penalized Poisson regression approach for subgroup analysis in claim frequency data is proposed. Subjects are assumed to follow a zero-inflated Poisson regression model with group-specific intercepts, which capture group characteristics of claim frequency. A penalized likelihood function is derived and optimized to identify the group-specific intercepts and effects of individual covariates. To handle the challenges arising from the optimization of the penalized likelihood function, an alternating direction method of multipliers algorithm is developed and its convergence is established. Simulation studies and real applications are provided for illustrations. 相似文献
924.
P. T. An 《Numerical Functional Analysis & Optimization》2019,40(8):944-952
We present an efficient algorithm for finding the shortest path joining two points in a sequence of triangles in three-dimensional space using the concept of funnels associated with common edges along the sequence of triangles and the planar unfolding for each funnel. We show that the unfolded image of a funnel is a simple polygon, it thus is non-overlapping. Therefore, such funnels are determined iteratively to their associated common edges by the planar unfolding and the shortest path joining two points is determined by cusps of these funnels. 相似文献
925.
Messaoud Boulbrachene 《Mathematical Methods in the Applied Sciences》2019,42(16):5305-5316
In this paper, we extend the approach developed by the author for the standard finite element method in the L∞‐norm of the noncoercive variational inequalities (VI) (Numer Funct Anal Optim.2015;36:1107‐1121.) to impulse control quasi‐variational inequality (QVI). We derive the optimal error estimate, combining the so‐called Bensoussan‐Lions Algorithm and the concept of subsolutions for VIs. 相似文献
926.
《Stochastic Processes and their Applications》2019,129(12):5278-5311
In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly overdamped) Langevin diffusion and establish guarantees on its error measured in the Wasserstein-2 distance. Our guarantees improve or extend the state-of-the-art results in three directions. First, we provide an upper bound on the error of the first-order Langevin Monte Carlo (LMC) algorithm with optimized varying step-size. This result has the advantage of being horizon free (we do not need to know in advance the target precision) and to improve by a logarithmic factor the corresponding result for the constant step-size. Second, we study the case where accurate evaluations of the gradient of the log-density are unavailable, but one can have access to approximations of the aforementioned gradient. In such a situation, we consider both deterministic and stochastic approximations of the gradient and provide an upper bound on the sampling error of the first-order LMC that quantifies the impact of the gradient evaluation inaccuracies. Third, we establish upper bounds for two versions of the second-order LMC, which leverage the Hessian of the log-density. We provide non asymptotic guarantees on the sampling error of these second-order LMCs. These guarantees reveal that the second-order LMC algorithms improve on the first-order LMC in ill-conditioned settings. 相似文献
927.
Point estimators for the parameters of the component lifetime distribution in coherent systems are evolved assuming to be independently and identically Weibull distributed component lifetimes. We study both complete and incomplete information under continuous monitoring of the essential component lifetimes. First, we prove that the maximum likelihood estimator (MLE) under complete information based on progressively Type‐II censored system lifetimes uniquely exists and we present two approaches to compute the estimates. Furthermore, we consider an ad hoc estimator, a max‐probability plan estimator and the MLE for the parameters under incomplete information. In order to compute the MLEs, we consider a direct maximization of the likelihood and an EM‐algorithm–type approach, respectively. In all cases, we illustrate the results by simulations of the five‐component bridge system and the 10‐component parallel system, respectively. 相似文献
928.
929.
Fernando De Tern Bruno Iannazzo Federico Poloni Leonardo Robol 《Numerical Linear Algebra with Applications》2019,26(5)
We consider the uniqueness of solution (i.e., nonsingularity) of systems of r generalized Sylvester and ?‐Sylvester equations with n×n coefficients. After several reductions, we show that it is sufficient to analyze periodic systems having, at most, one generalized ?‐Sylvester equation. We provide characterizations for the nonsingularity in terms of spectral properties of either matrix pencils or formal matrix products, both constructed from the coefficients of the system. The proposed approach uses the periodic Schur decomposition and leads to a backward stable O(n3r) algorithm for computing the (unique) solution. 相似文献
930.
Aaron J. Molstad Adam J. Rothman 《Journal of computational and graphical statistics》2019,28(1):11-22
We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrix estimators to have equal entries and also encourage zeros in the precision matrix estimator. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix. We show that our method can outperform relevant competitors in classification, even when our modeling assumptions are violated. We analyze three real datasets to demonstrate our method’s applicability. Supplementary materials, including an R package implementing our method, are available online. 相似文献