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Block coordinate descent with time perturbation for nonconvex nonsmooth problems in real-world studies

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Frontiers of Information Technology & Electronic Engineering 2019年第10期20卷 1390-1403页

作者： Rui LIU Wei-chu SUN Tao HOU Chun-hong HU Lin-bo QIAO Department of Oncology The Second Xiangya Hospital of Central South UniversityChangsha 410011China First Clinical Medical College University of South ChinaHengyang 421001China College of Computer National University of Defense TechnologyChangsha 410073China

The era of big data in healthcare is here, and this era will significantly improve medicine and especially oncology. However, traditional machine learning algorithms need to be promoted to solve such large-scale real-world problems due to a large amount of data that needs to be analyzed and the difficulty in solving problems with nonconvex nonlinear settings. We aim to minimize the composite of a smooth nonlinear function and a block-separable nonconvex function on a large number of block variables with inequality constraints. We propose a novel parallel first-order optimization method, called asynchronous block coordinate descent with time perturbation (ATP), which adopts a time perturbation technique that escapes from saddle points and sub-optimal local points. The details of the proposed method are presented with analyses of convergence and iteration complexity properties. Experiments conducted on real-world machine learning problems validate the efficacy of our proposed method. The experimental results demonstrate that time perturbation enables ATP to escape from saddle points and sub-optimal points, providing a promising way to handle nonconvex optimization problems with inequality constraints employing asynchronous block coordinate descent. The asynchronous parallel implementation on shared memory multi-core platforms indicates that the proposed algorithm, ATP, has strong scalability.

关键词： Convergence analysis Asynchronous block coordinate descent method Time perturbation Nonconvex nonsmooth optimization Real-world study

Optimum blade loading for a powered rotor in descent

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Chinese Journal of Aeronautics 2016年第3期29卷 580-584页

作者： Ramin Modarres David A.Peters Department of Mechanical Engineering & Materials Science Washington University in St.Louis

The optimum loading for rotors has previously been found for hover, climb and wind turbine conditions; but, up to now, no one has determined the optimum rotor loading in descent. This could be an important design consideration for rotary-wing parachutes and low-speed des- cents. In this paper, the optimal loading for a powered rotor in descent is found from momentum theory based on a variational principle. This loading is compared with the optimal loading for a rotor in hover or climb and with the Betz rotor loading （which is optimum for a lightly-loaded rotor）. Wake contraction for each of the various loadings is also presented.

关键词： descent HelicopterInflow Loading Optimum

SPECTRAL MAPPING THEOREM FOR ASCENT,ESSENTIAL ASCENT, descent AND ESSENTIAL descent SPECTRUM OF LINEAR RELATIONS

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Acta Mathematica Scientia 2014年第4期34卷 1212-1224页

作者： Ezzeddine CHAFAI Maher MNIF Departement of Mathematics Faculty of Sciences of SfaxUniversity of SfaxTunisia

In [7], Cross showed that the spectrum of a linear relation T on a normed space satisfies the spectral mapping theorem. In this paper, we extend the notion of essential ascent and descent for an operator acting on a vector space to linear relations acting on Banach spaces. We focus to define and study the descent, essential descent, ascent and essential ascent spectrum of a linear relation everywhere defined on a Banach space X. In particular, we show that the corresponding spectrum satisfy the polynomial version of the spectral mapping theorem.

关键词： ascent essential ascent descent essential descent linear relations

CONVERGENCE RATE OF GRADIENT descent METHOD FOR MULTI-OBJECTIVE OPTIMIZATION

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Journal of Computational Mathematics 2019年第5期37卷 689-703页

作者： Liaoyuan Zeng Yuhong Dai Yakui Huang Institute of Computational Mathematics and Scientific/Engineering Computing State Key Labomtory of Scientific and Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Science Hebei University of TechnologyTianjin 300401 China

The convergence rate of the gradient descent method is considered for unconstrained multi-objective optimization problems (MOP). Under standard assumptions, we prove that the gradient descent method with constant stepsizes converges sublinearly when the objective functions are convex and the convergence rate can be strengthened to be linear if the objective functions are strongly convex. The results are also extended to the gradient descent method with the Armijo line search. Hence, we see that the gradient descent method for MOP enjoys the same convergence properties as those for scalar optimization.

关键词： Multi-objective optimization Gradient descent Convergence rate.

Supervised descent method for weld pool boundary extraction during fiber laser welding process

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China Welding 2019年第1期28卷 6-10页

作者：赵耀邦张登明吴远峰杨长祺 Shanghai Spaceflight Precision Machinery Institute

In order to obtain a high-quality weld during the laser welding process, extracting the characteristic parameters of weld pool is an important issue for automated welding. In this paper, the type 304 austenitic stainless steel is welded by a 5 kW high-power fiber laser and a high-speed camera is employed to capture the topside images of weld pools. Then we propose a robust visual-detection approach for the molten pool based on the supervised descent method. It provides an elegant framework for representing the outline of a weld pool and is especially efficient for weld pool detection in the presence of strong uncertainties and disturbances. Finally, welding experimental results verified that the proposed approach can extract the weld pool boundary accurately, which will lay a solid foundation for controlling the weld quality of fiber laser welding process.

关键词： fiber laser welding molten pool supervised descent method boundary extraction

descent in Symmetry during Solid State Transitions and Other Anomalies in Mixed Valence Compounds AxMxⅡM1-xⅢF3(A = K, Rb, Cs;M = V, Cr;x = 0.0 - 1.0)

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Natural Science 2019年第6期11卷 221-232页

作者： William O.J.Boo Daniell L.Mattern Robert M.Metzger Department of Chemistry and Biochemistry University of MississippiUniversityMSUSA Department of Chemistry and Biochemistry University of AlabamaTuscaloosaALUSA

The scope of solid-state transitions, from melting temperatures down to 4.2 K, is described for six systems: KxVF3, RbxVF3, CsxVF3, KxCrF3, RbxCrF3, and CsxCrF3 (for x = 0.0 to 1.0). Connections are drawn between the compounds’ compositions and structures with the various transitions and ordering events. Upon solidification from the melt and gradual cooling to room temperature, a sequential descent of symmetry appears to occur, from high-symmetry perovskite phases, through possible reconstructive transitions, to phases designated α, β, and δ, within which ionic ordering finally sets in, forming many new lower-symmetry structures. Many stable new structures are seen at room temperature. Finally, at cryogenic temperatures, magnetic ordering sets in. Other anomalies for these systems are also described. The analysis underscores the overall correspondence of structure, composition, and magnetic properties in these compounds. This lowering of symmetry mirrors what has been chronicled for oxygen-bearing perovskites that have yielded so many high-temperature ceramic superconductors.

关键词： descent in Symmetry Ionic Ordering Magnetic Ordering Magnetic Susceptibility Reconstructive Transitions

Linear Regression and Gradient descent Method for Electricity Output Power Prediction

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Journal of Computer and Communications 2019年第12期7卷 31-36页

作者： Yuanliang Liao Tsinghua International School Campus of Tsinghua High School Beijing China

Regulating the power output for a power plant as demand for electricity fluctuates throughout the day is important for both economic purpose and the safety of the generator. In this work, gradient descent method together with regularization is investigated to study the electricity output related to vacuum level and temperature in the turbine. Ninety percent of the data was used to train the regression parameters while the remaining ten percent was used for validation. Final results showed that 99% accuracy could be obtained with this method. This opens a new window for electricity output prediction for power plants.

关键词： Machine Learning Linear Algebra Linear Regression Gradient descent Error Analysis

Antenna Array Pattern Synthesis via Coordinate descent Method

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Journal of Electromagnetic Analysis and Applications 2015年第5期7卷 168-177页

作者： Yuanhao Wang Xiaoxi He Jiangning Wang Sergey Berezin Wolfgang Mathis Institut für Theoretische Elektrotechnik Gottfried Wilhelm Leibniz Universitat Hannover Hannover Germany Applied Mathematics Department Saint-Petersburg State Polytechnical University St. Petersburg Russia

This paper presents an array pattern synthesis algorithm for arbitrary arrays based on coordinate descent method (CDM). With this algorithm, the complex element weights are found to minimize a weighted L2 norm of the difference between desired and achieved pattern. Compared with traditional optimization techniques, CDM is easy to implement and efficient to reach the optimum solutions. Main advantage is the flexibility. CDM is suitable for linear and planar array with arbitrary array elements on arbitrary positions. With this method, we can configure arbitrary beam pattern, which gives it the ability to solve variety of beam forming problem, e.g. focused beam, shaped beam, nulls at arbitrary direction and with arbitrary beam width. CDM is applicable for phase-only and amplitude-only arrays as well, and furthermore, it is a suitable method to treat the problem of array with element failures.

关键词： Antenna Phased Array Optimization Pattern Synthesis Coordinate descent Method

Efficacy of non-pharmacological interventions in controlling type 2 diabetes in patients of African descent: A systematic review

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Journal of Biomedical Science and Engineering 2013年第5期6卷 36-44页

作者： Takira Glasgow Liz Cheek Naji Tabet Computing Engineering and Mathematics University of Brighton Brighton UK Postgraduate Medicine Division of Medical Education Brighton and Sussex Medical School Brighton UK

Purpose: The purpose of this review is to systematically assess the potential effectiveness of targeted educational and other non-pharmacological interventions on diabetes control in populations of African descent in developed countries. Such information can inform intervention strategies and highlight evidence-based approaches to deal with this significant problem in this population. Methods: A systematic review and a meta-analysis of random controlled trials and cohort studies evaluating the influence of education and other non-pharmacological interventions on HbA1Cconcentrations in patients of African descent with diabetes. A comprehensive search of PubMed, EMBASE, CINAHL, ZETOC, SIGLE databases was carried out. Results: Although nine studies (8 randomised controlled trials and 1 cohort study) met the inclusion criteria, relevant HbA1Cdata were available for 6 of the studies for the subsequent meta-analysis. Heterogeneity of meta-analysis was high (I2 = 92%), the random effects pooled standard mean difference favoured the intervention -0.66 (-1.15, -0.17), p = 0.009. After sensitivity analysis, I2 remained moderate to high at 69%. The random effects pooled standard mean difference continued to favour the intervention -0.48 (-0.81, -0.16), p = 0.009. Conclusion: There is evidence supporting the efficacy of educational and other non-pharmacological interventions in diabetes control in populations of African descent in English speaking developed countries. This conclusion is tempered by the significant heterogeneity of selected interventions and paucity of high quality research in the target population.

关键词： Diabetes Education African descent Non-Pharmacological Intervention HbA1C