scholarly journals Probabilistic constrained optimization on flow networks

2021 ◽  
Author(s):  
Michael Schuster ◽  
Elisa Strauch ◽  
Martin Gugat ◽  
Jens Lang
Keyword(s):  
Boundary Data ◽  
Optimization Problems ◽  
Kernel Density ◽  
Necessary Optimality Conditions ◽  
Density Estimator ◽  
Dynamic Flow ◽  
Random Boundary ◽  
Flow Problems ◽  
Advantages And Disadvantages ◽  
Dynamic Flow Model

AbstractUncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and a dynamic flow model with uncertain boundary data on networks. We introduce two different ways how to compute the probability for random boundary data to be feasible, discussing their advantages and disadvantages. In this context, feasible means, that the flow corresponding to the random boundary data meets some box constraints at the network junctions. The first method is the spheric radial decomposition and the second method is a kernel density estimation. In both settings, we consider certain optimization problems and we compute derivatives of the probabilistic constraint using the kernel density estimator. Moreover, we derive necessary optimality conditions for an approximated problem for the stationary and the dynamic case. Throughout the paper, we use numerical examples to illustrate our results by comparing them with a classical Monte Carlo approach to compute the desired probability.

Review of Network Flow Algorithms David P. Williamson

2021 ◽  
Vol 52 (1) ◽  
pp. 12-15
Author(s):  
S.V. Nagaraj
Keyword(s):  
Graduate Students ◽  
Real World ◽  
Network Flow ◽  
Network Flows ◽  
Optimization Problems ◽  
Capacity Constraints ◽  
Incoming Flow ◽  
Network Flow Problems ◽  
Flow Problems ◽  
Real World Problems

This book is on algorithms for network flows. Network flow problems are optimization problems where given a flow network, the aim is to construct a flow that respects the capacity constraints of the edges of the network, so that incoming flow equals the outgoing flow for all vertices of the network except designated vertices known as the source and the sink. Network flow algorithms solve many real-world problems. This book is intended to serve graduate students and as a reference. The book is also available in eBook (ISBN 9781316952894/US$ 32.00), and hardback (ISBN 9781107185890/US$99.99) formats. The book has a companion web site www.networkflowalgs.com where a pre-publication version of the book can be downloaded gratis.

scholarly journals Intra-urban differentials of congenital and acquired syphilis and syphilis in pregnant women in an urban area in northeastern Brazil

2021 ◽  
Author(s):  
Talita Araujo de Souza ◽  
Karen Kaline Teixeira ◽  
Reginaldo Lopes Santana ◽  
Cinthia Barros Penha ◽  
Arthur de Almeida Medeiros ◽  
...  
Keyword(s):  
Relative Risk ◽  
Pregnant Women ◽  
Congenital Syphilis ◽  
Kernel Density ◽  
Poisson Model ◽  
Northeastern Brazil ◽  
Smoothing Function ◽  
Density Estimator ◽  
Epidemic Disease ◽  
Peripheral Areas

Abstract Background Currently syphilis is considered an epidemic disease worldwide. The objective of this study was to identify intra-urban differentials in the occurrence of congenital and acquired syphilis and syphilis in pregnant women in the city of Natal, in northeast Brazil. Methods Cases of syphilis recorded by the municipal surveillance system from 1 January 2011 to 30 December 2018 were analysed. Spatial statistical analyses were performed using the kernel density estimator of the quadratic smoothing function (weighted). SaTScan software was applied for the calculation of risk based on a discrete Poisson model. Results There were 2163 cases of acquired syphilis, 738 cases of syphilis in pregnant women and 1279 cases of congenital syphilis. Kernel density maps showed that the occurrence of cases is more prevalent in peripheral areas and in areas with more precarious urban infrastructure. In 2011–2014 and 2015–2018, seven statistically significant clusters of acquired syphilis were identified. From 2011 to 2014, the most likely cluster had a relative risk of 3.54 (log likelihood ratio [LLR] 38 895; p<0.001) and from 2015 to 2018 the relative risk was 0.54 (LLR 69 955; p<0.001). Conclusions In the municipality of Natal, there was a clustered pattern of spatial distribution of syphilis, with some areas presenting greater risk for the occurrence of new cases.

scholarly journals Analysis of the spatial distribution of dengue cases in the city of Rio de Janeiro, 2011 and 2012

2017 ◽  
Vol 51 ◽  
Author(s):  
Silvia Carvalho ◽  
Mônica De Avelar Figueiredo Mafra Magalhães ◽  
Roberto De Andrade Medronho
Keyword(s):  
Information System ◽  
Spatial Distribution ◽  
Rio De Janeiro ◽  
Influencing Factor ◽  
Kernel Density ◽  
Severe Dengue ◽  
Automatic Process ◽  
Density Estimator ◽  
Macroeconomic Policies ◽  
The City

OBJECTIVE Analyze the spatial distribution of classical dengue and severe dengue cases in the city of Rio de Janeiro. METHODS Exploratory study, considering cases of classical dengue and severe dengue with laboratory confirmation of the infection in the city of Rio de Janeiro during the years 2011/2012. The georeferencing technique was applied for the cases notified in the Notification Increase Information System in the period of 2011 and 2012. For this process, the fields “street” and “number” were used. The ArcGis10 program’s Geocoding tool’s automatic process was performed. The spatial analysis was done through the kernel density estimator. RESULTS Kernel density pointed out hotspots for classic dengue that did not coincide geographically with severe dengue and were in or near favelas. The kernel ratio did not show a notable change in the spatial distribution pattern observed in the kernel density analysis. The georeferencing process showed a loss of 41% of classic dengue registries and 17% of severe dengue registries due to the address in the Notification Increase Information System form. CONCLUSIONS The hotspots near the favelas suggest that the social vulnerability of these localities can be an influencing factor for the occurrence of this aggravation since there is a deficiency of the supply and access to essential goods and services for the population. To reduce this vulnerability, interventions must be related to macroeconomic policies.

Review of Rainfall Data Application for Design and Analysis

1984 ◽  
Vol 16 (8-9) ◽  
pp. 1-45 ◽  
Author(s):  
V Arnell ◽  
P Harremoës ◽  
M Jensen ◽  
N B Johansen ◽  
J Niemczynowicz
Keyword(s):  
Statistical Prediction ◽  
Dynamic Flow ◽  
Combined Sewer Overflows ◽  
Statistical Characterization ◽  
Data Application ◽  
Combined Sewer ◽  
Dynamic Flow Model ◽  
Receiving Waters ◽  
Rain Fall

This review has been prepared for the international seminar: Rain fall as the basis for urban runoff design and analysis, held in Copenhagen, 24'26 Aug. 1983. The purpose of the review is to bring a state of the art within, 1) the statistical characterization of rain fall in time and space, 2) the development of synthetic design storms and, 3) the application of both synthetic design storms and historical storms to pipe design, flooding prediction, design of detention basins and calculation of the yearly or extreme pollutiona1 load on receiving waters from combined sewer overflows. The main conclusion, primarily related to item 3), is that more attention in this context should be put on statistical analysis of the detrimental effects: flooding and pollution. This analysis is best performed by applying historical rain records. Realistic flooding prediction is believed only to be possible with a fully dynamic flow model, whereas pollution may be studied by means of simpler models like the time area approach. The outstanding problem in the statistical prediction is the distribution in space of the historical rains.

scholarly journals Minimum Principle-Type Necessary Optimality Conditions in Scalar and Vector Optimization. An Account

2017 ◽  
Vol 9 (4) ◽  
pp. 168
Author(s):  
Giorgio Giorgi
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Minimum Principle ◽  
Necessary Optimality Conditions ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Scalar Optimization ◽  
Scalar And Vector Optimization

We take into condideration necessary optimality conditions of minimum principle-type, that is for optimization problems having, besides the usual inequality and/or equality constraints, a set constraint. The first part pf the paper is concerned with scalar optimization problems; the second part of the paper deals with vector optimization problems.

scholarly journals On implicit variables in optimization theory

2021 ◽  
Vol Volume 2 (Original research articles) ◽  
Author(s):  
Matúš Benko ◽  
Patrick Mehlitz
Keyword(s):  
Optimization Problems ◽  
Constraint Qualifications ◽  
Optimization Theory ◽  
Mathematical Optimization ◽  
General Setting ◽  
Necessary Optimality Conditions ◽  
Detailed Comparison ◽  
Mordukhovich Stationarity ◽  
Stationarity Conditions ◽  
The One

Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel programming, evaluated multiobjective optimization, or nonlinear optimization problems with slack variables. In order to deal with implicit variables, they are often interpreted as explicit ones. Here, we first point out that this is a light-headed approach which induces artificial locally optimal solutions. Afterwards, we derive various Mordukhovich-stationarity-type necessary optimality conditions which correspond to treating the implicit variables as explicit ones on the one hand, or using them only implicitly to model the constraints on the other. A detailed comparison of the obtained stationarity conditions as well as the associated underlying constraint qualifications will be provided. Overall, we proceed in a fairly general setting relying on modern tools of variational analysis. Finally, we apply our findings to different well-known problem classes of mathematical optimization in order to visualize the obtained theory. Comment: 34 pages

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