scholarly journals Graphical Convergence of Subgradients in Nonconvex Optimization and Learning

2021 ◽  
Author(s):  
Damek Davis ◽  
Dmitriy Drusvyatskiy
Keyword(s):  
Generalized Linear Model ◽  
Optimization Problem ◽  
Full Generality ◽  
Regression Problem ◽  
Smooth Maps ◽  
Sample Average Approximations ◽  
Sample Average ◽  
Stochastic Optimization Problem ◽  
Estimation Quality

We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the primary examples of such losses. We analyze the estimation quality of such nonsmooth and nonconvex problems by their sample average approximations. Our main results establish dimension-dependent rates on subgradient estimation in full generality and dimension-independent rates when the loss is a generalized linear model. As an application of the developed techniques, we analyze the nonsmooth landscape of a robust nonlinear regression problem.

Imaging through Scattering Media with a Learning Based Prior

2020 ◽  
Vol 2020 (14) ◽  
pp. 306-1-306-6
Author(s):  
Florian Schiffers ◽  
Lionel Fiske ◽  
Pablo Ruiz ◽  
Aggelos K. Katsaggelos ◽  
Oliver Cossairt
Keyword(s):  
Optimization Problem ◽  
Autonomous Driving ◽  
Scattering Media ◽  
Photon Scattering ◽  
Point Spread ◽  
Spread Function ◽  
Radiative Transport Equation ◽  
Spatio Temporal ◽  
Transient Imaging

Imaging through scattering media finds applications in diverse fields from biomedicine to autonomous driving. However, interpreting the resulting images is difficult due to blur caused by the scattering of photons within the medium. Transient information, captured with fast temporal sensors, can be used to significantly improve the quality of images acquired in scattering conditions. Photon scattering, within a highly scattering media, is well modeled by the diffusion approximation of the Radiative Transport Equation (RTE). Its solution is easily derived which can be interpreted as a Spatio-Temporal Point Spread Function (STPSF). In this paper, we first discuss the properties of the ST-PSF and subsequently use this knowledge to simulate transient imaging through highly scattering media. We then propose a framework to invert the forward model, which assumes Poisson noise, to recover a noise-free, unblurred image by solving an optimization problem.

scholarly journals Joint optimization of computing ratio and access points’ density for mixed mobile edge/cloud computing

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tianqi Jing ◽  
Shiwen He ◽  
Fei Yu ◽  
Yongming Huang ◽  
Luxi Yang ◽  
...  
Keyword(s):  
Cloud Computing ◽  
Coverage Probability ◽  
Optimization Problem ◽  
Mobile Cloud Computing ◽  
Low Complexity ◽  
Mixed Integer ◽  
Joint Optimization ◽  
Mobile Cloud ◽  
Convex Problem

AbstractCooperation between the mobile edge computing (MEC) and the mobile cloud computing (MCC) in offloading computing could improve quality of service (QoS) of user equipments (UEs) with computation-intensive tasks. In this paper, in order to minimize the expect charge, we focus on the problem of how to offload the computation-intensive task from the resource-scarce UE to access point’s (AP) and the cloud, and the density allocation of APs’ at mobile edge. We consider three offloading computing modes and focus on the coverage probability of each mode and corresponding ergodic rates. The resulting optimization problem is a mixed-integer and non-convex problem in the objective function and constraints. We propose a low-complexity suboptimal algorithm called Iteration of Convex Optimization and Nonlinear Programming (ICONP) to solve it. Numerical results verify the better performance of our proposed algorithm. Optimal computing ratios and APs’ density allocation contribute to the charge saving.

Engine Mount Optimization for Vibration Isolation in Motorcycles

2006 ◽  
Author(s):  
Sudhir Kaul ◽  
Anoop K. Dhingra ◽  
Timothy G. Hunter
Keyword(s):  
Optimization Problem ◽  
Vibration Isolation ◽  
Total Force ◽  
Engine Mounts ◽  
The Road ◽  
Design Variables ◽  
Swing Arm ◽  
Engine Mount ◽  
Six Degree Of Freedom

This paper presents a comprehensive model to capture the dynamics of a motorcycle system in order to evaluate the quality of vibration isolation. The two main structural components in the motorcycle assembly - the frame and the swing-arm - are modeled using reduced order finite element models; the power-train assembly is modeled as a six degree-of-freedom (DOF) rigid body connected to the frame through the engine mounts and to the swing-arm through a shaft assembly. The engine mounts are modeled as tri-axial spring-damper systems. Models of the front-end assembly as well as front and rear tires are also included in the overall model. The complete vehicle model is used to solve the engine mount optimization problem so as to minimize the total force transmitted to the frame while meeting packaging and other side constraints. The mount system parameters - stiffness, position and orientation vectors - are used as design variables for the optimization problem. The imposed loads include forces and moments due to engine imbalance as well as loads transmitted due to irregularities in the road surface through the tire patch.

scholarly journals A RED modified weighted moving average for soft real-time application

2014 ◽  
Vol 24 (3) ◽  
pp. 697-707 ◽  
Author(s):  
Joanna Domanśka ◽  
Adam Domański ◽  
Dariusz R. Augustyn ◽  
Jerzy Klamka
Keyword(s):  
Real Time ◽  
Optimization Problem ◽  
Optimality Criterion ◽  
Task Force ◽  
Moving Average ◽  
Timing Constraints ◽  
Real Time Traffic ◽  
Real Time Application ◽  
Weighted Moving Average

Abstract The popularity of TCP/IP has resulted in an increase in usage of best-effort networks for real-time communication. Much effort has been spent to ensure quality of service for soft real-time traffic over IP networks. The Internet Engineering Task Force has proposed some architecture components, such as Active Queue Management (AQM). The paper investigates the influence of the weighted moving average on packet waiting time reduction for an AQM mechanism: the RED algorithm. The proposed method for computing the average queue length is based on a difference equation (a recursive equation). Depending on a particular optimality criterion, proper parameters of the modified weighted moving average function can be chosen. This change will allow reducing the number of violations of timing constraints and better use of this mechanism for soft real-time transmissions. The optimization problem is solved through simulations performed in OMNeT++ and later verified experimentally on a Linux implementation

scholarly journals Development and validation of the predictive risk of death model for adult patients admitted to intensive care units in Japan: an approach to improve the accuracy of healthcare quality measures

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Hideki Endo ◽  
Shigehiko Uchino ◽  
Satoru Hashimoto ◽  
Yoshitaka Aoki ◽  
Eiji Hashiba ◽  
...  
Keyword(s):  
Intensive Care ◽  
Quality Of Care ◽  
Generalized Linear Model ◽  
Healthcare Quality ◽  
Brier Score ◽  
Linear Predictor ◽  
Risk Of Death ◽  
Apache Iii ◽  
Funnel Plots

Abstract Background The Acute Physiology and Chronic Health Evaluation (APACHE) III-j model is widely used to predict mortality in Japanese intensive care units (ICUs). Although the model’s discrimination is excellent, its calibration is poor. APACHE III-j overestimates the risk of death, making its evaluation of healthcare quality inaccurate. This study aimed to improve the calibration of the model and develop a Japan Risk of Death (JROD) model for benchmarking purposes. Methods A retrospective analysis was conducted using a national clinical registry of ICU patients in Japan. Adult patients admitted to an ICU between April 1, 2018, and March 31, 2019, were included. The APACHE III-j model was recalibrated with the following models: Model 1, predicting mortality with an offset variable for the linear predictor of the APACHE III-j model using a generalized linear model; model 2, predicting mortality with the linear predictor of the APACHE III-j model using a generalized linear model; and model 3, predicting mortality with the linear predictor of the APACHE III-j model using a hierarchical generalized additive model. Model performance was assessed with the area under the receiver operating characteristic curve (AUROC), the Brier score, and the modified Hosmer–Lemeshow test. To confirm model applicability to evaluating quality of care, funnel plots of the standardized mortality ratio and exponentially weighted moving average (EWMA) charts for mortality were drawn. Results In total, 33,557 patients from 44 ICUs were included in the study population. ICU mortality was 3.8%, and hospital mortality was 8.1%. The AUROC, Brier score, and modified Hosmer–Lemeshow p value of the original model and models 1, 2, and 3 were 0.915, 0.062, and < .001; 0.915, 0.047, and < .001; 0.915, 0.047, and .002; and 0.917, 0.047, and .84, respectively. Except for model 3, the funnel plots showed overdispersion. The validity of the EWMA charts for the recalibrated models was determined by visual inspection. Conclusions Model 3 showed good performance and can be adopted as the JROD model for monitoring quality of care in an ICU, although further investigation of the clinical validity of outlier detection is required. This update method may also be useful in other settings.

scholarly journals USING THE METHOD OF SEQUENTIAL RESTRICTIONS FOR SOLVING A DUAL-OBJECTIVE PROBLEM OF PRODUCTION PLANNING

2020 ◽  
Vol 11 (87) ◽  
Author(s):  
Nataliia Dovha ◽  
◽  
Hryhorii Tsehelyk ◽  
Keyword(s):  
Optimization Problem ◽  
Production Efficiency ◽  
Point Of View ◽  
Main Task ◽  
Production Plan ◽  
Optimal Production ◽  
Economic Point ◽  
Use Of Resources ◽  
Maximum Profit

The processes of optimization of the production plan according to certain criteria by modeling were investigated. Achieving effective results directly depends on the optimal production plan. The most important thing in determining the optimal production plan is the choice of modeling criteria. For the most part, the quality of decisions is characterized not by one but by many incomparable criteria. Therefore, it is necessary to make decisions based not on one but on many criteria. This so-called multi-objective optimization problem. For solving such problems is widely used mathematical methods. Mathematical approach can be used to solve problems in any particular activity as mathematics abstracted from specific features characteristic of a particular solution. Therefore, from the point of view of mathematics, the optimal result can be obtained with various established criteria, but from the economic point of view it is important to choose the ones that are of decisive importance. That is, their weight is important for the consumer when making a purchase decision, and for the manufacturer – in terms of production capabilities of certain types and results (production efficiency). The basis of the operation of any enterprise is a production program (production and sales plan). The main task of the production plan is to meet the needs of consumers in high-quality products, which are produced with the best use of resources, on the one hand, and the enterprise to get the maximum profit, on the other. With this in mind, a two-criteria optimization model that allows to make a production plan was proposed. The plan ensures that products are produced with the best use of available resources and at the same time ensures maximum quality of manufactured products and maximum profit from sales of these products. The solution of the problem with two objective functions and linear constraints is achieved by step-by-step solution of the proposed mathematical model of optimization of the production plan using the method of sequential restrictions. The simplex method was also used. An example shows an algorithm for solving the optimization problem.

scholarly journals Information technology for time series forecasting by the method of the forecast scheme synthesis

2021 ◽  
Vol 3 (2) ◽  
pp. 81-86
Author(s):  
O. Yu. Mulesa ◽  
◽  
F. E. Geche ◽  
A. Ye. Batyuk ◽  
O. O. Melnyk ◽  
...  
Keyword(s):  
Information Technology ◽  
Time Series ◽  
Linear Combination ◽  
Optimization Problem ◽  
Quality Criterion ◽  
Quality Criteria ◽  
Time Series Forecasting ◽  
Percentage Error ◽  
Forecast Models

The study is devoted to the development of information technology for forecasting based on time series. It has been found that it is important to develop new models and forecasting methods to improve the quality of the forecast. Information technology is based on the evolutionary method of synthesis of the forecast scheme grounded on basic forecast models. The selected method allows you to consider any number of predictive models that may belong to different classes. For a given time series, the weight coefficients with which the models are included in the resulting forecast scheme are calculated by finding the solution to the optimization problem. The method of constructing the objective function for the optimization problem in the form of a linear combination of forecasting results by basic forecasting models is shown. It is proposed to find the solution to the optimization problem using a genetic algorithm. The result of the method is the forecast scheme, which is a linear combination of basic forecast models. To assess the quality of the forecast, it is suggested to use forecasting errors or forecast volatility calculated as the standard deviation. Forecast quality criteria are selected depending on the context of the task. The use of forecast volatility as a quality criterion, with repeated use of technology, will reduce the deviation of forecast values from real data. The structural scheme of information technology is developed. Structurally, information technology consists of two blocks: data processing and interpretation of the obtained values. The result of the application of the developed information technology is the production rules for determining the predicted value of the studied quantity. Experimental verification of the obtained results was performed. The problem of forecasting the number of religious organizations in Ukraine based on statistical data from 1997 to 2000 has been solved. The autoregression method and the linear regression model were chosen as the basic forecast models. Based on the results of using the developed information technology, the weights of the basic models were calculated. It is demonstrated that the obtained forecast scheme allowed to improve the average absolute percentage error and forecast volatility in comparison with the selected models. Keywords: information technology; time series; forecasting; evolutionary technologies; forecast volatility; synthesis of the forecast scheme.

Optimal Use of GNSS Spacecraft in SBAS and GBAS Functional Augmentations

2021 ◽  
Vol 8 (4) ◽  
pp. 31-35
Author(s):  
V. V. Kurshin ◽  
◽  
D. V. Filimonova ◽  
Keyword(s):  
Optimization Problem ◽  
Maximum Efficiency ◽  
Gps Satellites ◽  
Gnss Measurements ◽  
Navigation Service ◽  
Optimal Set

The article discusses a method for improving the quality of navigation services for consumers with increased requirements for accuracy and reliability using satellite-based augmentation systems (SBAS) and ground-based augmentation systems (GBAS). Augmentation systems provide users with corrections that are used to correct GNSS measurements and integrity information. Due to the existing restrictions on the number of satellites for which corrections are transmitted, the article proposes the optimal use of GPS satellites, which is an incomplete set of 27 satellites that will be used in the GLONASS/GPS/SBAS navigation service, while measurements of the full constellation of GLONASS satellites are used for positioning. It is proposed to carry out the choice of 27 from the existing constellation of 32 GPS satellites in such a way that the subsystem provides the maximum efficiency of using the GNSS signals. The optimization problem or finding the optimal set of excluded GNSS satellites is solved according to R. Bellman’s algorithm. The found optimal set of excluded GNSS satellites makes it possible to reduce VDOP in comparison with the non-optimal one by almost 24 % and thereby improve navigation performance using GLONASS/GPS signals and SBAS corrections.

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