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∈-subgradient algorithms for bilevel convex optimization

Inverse Problems 2017年第5期33卷

作者： Helou, Elias S. Simões, Lucas E.A. Department of Applied Mathematics and Statistics Institute of Mathematical Sciences and Computation USP São Carlos Brazil Institute of Mathematics Statistics and Scientific Computing UNICAMP Campinas Brazil

This paper introduces and studies the convergence properties of a new class of explicit ∈-subgradient methods for the task of minimizing a convex function over a set of minimizers of another convex minimization problem. The general algorithm specializes to some important cases, such as first-order methods applied to a varying objective function, which have computationally cheap iterations. We present numerical experimentation concerning certain applications where the theoretical framework encompasses efficient algorithmic techniques, enabling the use of the resulting methods to solve very large practical problems arising in tomographic image reconstruction. © 2017 IOP Publishing Ltd.

关键词： Convex optimization

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Morphological perceptron learning

Morphological perceptron learning

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IEEE International Symposium on Intelligent Control (ISIC)

作者： P. Sussner Institute for Mathematics Statisticsand Scientific Computation Department of Applied Mathematics State University of Campinas Sao Paulo Brazil

Perceptrons have been used to classify patterns into different classes. Several researchers introduced a novel class of artificial neural networks, called morphological neural networks. In this new theory, the first step in computing the next state of a neuron or in performing the next layer neural network computation involves the nonlinear operation of adding neural values and their synaptic strengths followed by forming the maximum of the results. Ritter et al. (1997) have shown that the properties of morphological neural networks differ drastically from those of traditional neural network models. In this paper, the author introduces a learning algorithm for multilayer morphological perceptrons which is capable of solving arbitrary classification problems of patterns into two classes.

关键词： Neural networks Artificial neural networks Computer networks Multi-layer neural network Neurons Biological system modeling Electric potential Algebra mathematics Mathematical model

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The TSTT mesh interface

The TSTT mesh interface

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44th AIAA Aerospace Sciences Meeting 2006

作者： Ollivier-Gooch, Carl Chand, Kyle Dahlgren, Tamara Diachin, Lori Freitag Fix, Brian Kraftcheck, Jason Xiaolin, Li Seol, E. Seegyoung Shephard, Mark S. Tautges, Timothy Trease, Harold Advanced Numerical Simulation Laboratory University of British Columbia Center for Applied Scientific Computing Lawrence Livermore National Laboratory Dept. of Applied Mathematics and Statistics SUNY Stonybrook Parallel Computing Sciences Sandia National Laboratories Scientific Computation Research Center Rensselaer Polytechnic Institute Pacific Northwest National Laboratory

ISBN: (纸本)1563478072

PDE-based numerical simulation applications commonly use basic software infrastructure to manage mesh, geometry, and discretization data. The commonality of this infrastructure implies the software is theoretically amenable to re-use. However, the traditional reliance on library-based implementations of these functionalities hampers experimentation with different software instances that provide similar functionality. This is especially true for meshing and geometry libraries where applications often directly access the underlying data structures, which can be quite different from implementation to implementation. Thus, using different libraries interchangeably or interoperably for this functionality has proven difficult at best and has hampered the wide spread use of advanced meshing and geometry tools developed by the research community. To address these issues, the Terascale Simulation Tools and Technologies center is working to develop standard interfaces to enable the creation of interoperable and interchangeable simulation tools. In this paper, we focus on a language-and data-structure-independent interface supporting query and modification of mesh data conforming to a general abstract data model. We describe the model and interface, and provide programming "best practices" recommendations based on early experience implementing and using the interface.

关键词： Software engineering

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A family of growth models for representing the price process in online auctions 07

A family of growth models for representing the price process...

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Proceedings of the ninth international conference

作者： Hyde, Valerie Jank, Wolfgang Shmueli, Galit Applied Mathematics and Scientific Computation Program University of Maryland College Park MD 20742 Decision and Information Technologies Department Robert H. Smith School of Business University of Maryland College Park MD 20742

ISBN: (纸本)1595937005

Bids during an online auction arrive at unequally-spaced discrete time points. Our goal is to capture the entire continuous price-evolution function by representing it as a functional object. Various nonparametric smoothing methods exist to recover the functional object from the observed discrete bid data. Previous studies use penalized polynomial and monotone smoothing splines;however, these require the determination and storage of a large number of coefficients and often lengthy computational time. We present a family of parametric growth curves that describe the price-evolution during online auctions. This approach is parsimonious and has an appealing interpretation in the online auction context. We also provide an automated fitting algorithm that is computationally fast. Methods are illustrated using eBay data. Copyright 2007 ACM.

关键词： Cost accounting

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Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian

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Advances in applied mathematics and Mechanics 2023年第6期15卷 1631-1654页

作者： Jiaqi Zhang Yin Yang Zhaojie Zhou School of Mathematics and Computational Science Xiangtan UniversityHunan Key Laboratory for Computation and Simulation in Science and EngineeringKey Laboratory of Intelligent Computing and Information Processing of Ministry of EducationXiangtan 411105HunanChina School of Mathematics and Computational Science Xiangtan UniversityNational Center for Applied Mathematics in HunanHunan International Scientific and Technological Innovation Cooperation Base of Computational ScienceXiangtan 411105HunanChina School of Mathematics and Statistics Shandong Normal UniversityJinan 250014ShandongChina

In this paper spectral Galerkin approximation of optimal control problem governed by fractional elliptic equation is *** deal with the nonlocality of fractional Laplacian operator the Caffarelli-Silvestre extension is *** first order optimality condition of the extended optimal control problem is derived.A spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre polynomials is developed.A priori error estimates for the spectral Galerkin discrete scheme is *** experiments are presented to show the effectiveness of our methods and to verify the theoretical findings.

关键词： Fractional Laplacian optimal control problem Caffarelli-Silvestre extension weighted Laguerre polynomials

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ϵ-subgradient algorithms for bilevel convex optimization

arXiv

引用

arXiv 2017年

作者： Helou, Elias S. Simões, Lucas E.A. Department of Applied Mathematics and Statistics Institute of Mathematical Sciences and Computation - USP São Carlos Singapore Institute of Mathematics Statistics and Scientific Computing - UNICAMP Campina Brazil

This paper introduces and studies the convergence properties of a new class of explicit ϵ-subgradient methods for the task of minimizing a convex function over the set of minimizers of another convex minimization problem. The general algorithm specializes to some important cases, such as first-order methods applied to a varying objective function, which have computationally cheap iterations. We present numerical experimentation regarding certain applications where the theoretical framework encompasses efficient algorithmic techniques, enabling the use of the resulting methods to solve very large practical problems arising in tomographic image reconstruction. Copyright © 2017, The Authors. All rights reserved.

关键词： Convex optimization

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On the Ψ -fractional integral and applications

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computational and applied mathematics 2019年第1期38卷 1页

作者： Vanterler da C. Sousa, J. Capelas de Oliveira, E. Department of Applied Mathematics Institute of Mathematics Statistics and Scientific Computation Imecc-Unicamp Campinas rua Sérgio Buarque de Holanda 651 CampinasSP13083-859 Brazil

Motivated by the Ψ -Riemann–Liouville (Ψ - RL) fractional derivative and by the Ψ -Hilfer (Ψ - H) fractional derivative, we introduced a new fractional operator the so-called Ψ -fractional integral. We present some important results by means of theorems and in particular, that the Ψ -fractional integration operator is limited. In this sense, we discuss some examples, in particular, involving the Mittag–Leffler (M - L) function, of paramount importance in the solution of population growth problem, as approached. On the other hand, we realize a brief discussion on the uniqueness of nonlinear Ψ -fractional Volterra integral equation (VIE) using β-distance functions. © 2019, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.

关键词： Population statistics

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Estimating functional agent-based models: An application to bid shading in online markets format 11

Estimating functional agent-based models: An application to ...

引用

13th Annual Genetic and Evolutionary computation Conference - Companion Publication, GECCO 2011 Companion

作者： Guo, Wei Jank, Wolfgang Rand, William Applied Mathematics and Statistics and Scientific Computation Program Department of Mathematics University of Maryland College Park MD United States Department of Decision Operations and Information Technology Robert H. Smith School of Business University of Maryland College Park MD United States Department of Marketing Robert H. Smith School of Business University of Maryland College Park MD United States

ISBN: (纸本)9781450306904

Bid shading is a common strategy in online auctions to avoid the "winner's curse". While almost all bidders shade their bids, at least to some degree, it is impossible to infer the degree and volume of shaded bids directly from observed bidding data. In fact, most bidding data only allows us to observe the resulting price process, i.e. whether prices increase fast (due to little shading) or whether they slow down (when all bidders shade their bids). In this work, we propose an agent-based model that simulates bidders with different bidding strategies and their interaction with one another. We calibrate that model (and hence estimate properties about the propensity and degree of shaded bids) by matching the emerging simulated price process with that of the observed auction data using genetic algorithms. From a statistical point of view, this is challenging because we match functional draws from simulated and real price processes. We propose several competing fitness functions and explore how the choice alters the resulting ABM calibration. We apply our model to the context of eBay auctions for digital cameras and show that a balanced fitness function yields the best results. © 2011 ACM.

关键词： Calibration

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Online traffic light control through gradient estimation using stochastic fluid models

Online traffic light control through gradient estimation usi...

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作者： Panayiotou, Christos G. Howell, William C. Fu, Michael Department of Electrical and Computer Engineering University of Cyprus Nicosia Cyprus Applied Mathematics Scientific Computation Program Department of Mathematics University of Maryland College Park MD 20742 United States Smith School of Business and Institute for Systems Research University of Maryland College Park MD 20742 United States

ISBN: (纸本)008045108X

in this paper, we consider the problem of dynamically regulating the timing of traffic light controllers in busy cities. We use a Stochastic Fluid Model (SFM) to model the dynamics of the queues formed at an intersection. Based on this model, we derive gradients of the queue lengths with respect to the green/red light lengths within a signal cycle. We report preliminary numerical results comparing the performance of the estimates with finite-difference and smoothed perturbation analysis estimates. Then all estimators are used to optimize the traffic system via Stochastic Approximation. Copyright © 2005 IFAC.

关键词： Stochastic systems

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Estimation of mask effectiveness perception for small domains using multiple data sources

arXiv

引用

arXiv 2021年

作者： Sen, Aditi Lahiri, Partha Applied Mathematics & Statistics and Scientific Computation University of Maryland College Park United States The Joint Program in Survey Methodology Department of Mathematics University of Maryland College ParkMD20742 United States

All pandemics are local;so learning about the impacts of pandemics on public health and related societal issues at granular levels is of great interest. COVID-19 is affecting everyone in the globe and mask wearing is one of the few precautions against it. To quantify people's perception of mask effectiveness and to prevent the spread of COVID-19 for small areas, we use Understanding America Study's (UAS) survey data on COVID-19 as our primary data source. Our data analysis shows that direct survey-weighted estimates for small areas could be highly unreliable. In this paper, we develop a synthetic estimation method to estimate proportions of mask effectiveness for small area using a logistic model that combines information from multiple data sources. We select our working model using an extensive data analysis facilitated by a new variable selection criterion for survey data and benchmarking ratios. We propose a jackknife method to estimate variance of our proposed estimator. From our data analysis, it is evident that our proposed synthetic method outperforms direct survey-weighted estimator with respect to commonly used evaluation measures. Copyright © 2021, The Authors. All rights reserved.

关键词： Data handling

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