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1 edition of Dynamic factorization in large-scale optimization found in the catalog.

Dynamic factorization in large-scale optimization

Michael P. Olson

Dynamic factorization in large-scale optimization

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Published by Naval Postgraduate School, Available from the National Technical Information Service in Monterey, Calif, Springfield, Va .
Written in English


Edition Notes

ContributionsBrown, Gerald Gerard
The Physical Object
Pagination174 p.
Number of Pages174
ID Numbers
Open LibraryOL25526330M

challenges in dealing with large-scale data sets. First, the sheer volume and dimensionality of data make it often impossible to run analytics and traditional inferential methods using stand-alone processors, e.g., [8] and [31]. Decentralized learning with parallelized multicores is preferred [9], [22], while the data. Secrets of Matrix Factorization: Approximations, Numerics, Manifold Optimization and Random Restarts Je Hyeong Hong University of Cambridge [email protected] Andrew Fitzgibbon Microsoft, Cambridge, UK [email protected] Abstract Matrix factorization (or low-rank matrix completion) with missing data is a key computation in many computer. tributed, large-scale matrix factorization. We adapt the SGLD up-dates to make them suitable for distributed learning on subsets of users and products (or blocks). Each worker manages only a small block of the rating matrix, and updates and communicates only a small subset of the parameters in a fully-asynchronous or weakly-synchronous Size: KB.


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Dynamic factorization in large-scale optimization by Michael P. Olson Download PDF EPUB FB2

Factorization of linear programming (LP) models enables a large portion of the LP tableau to be represented implicitly and generated from the remaining explicit part. Dynamic factorization admits algebraic elements which change in dimension during the course of solution.

A unifying mathematical framework for dynamic row factorization is presented with three algorithms which derive from Cited by: Full text of "Dynamic factorization in large-scale optimization." See other formats. The primary obstacles facing such an approach are the large size of the formulation resulting from the linearization of the quadratic objective function and the poor quality of the lower bounds.

Special purpose linear programming methods using dynamic matrix factorization provide a promising avenue for solving these large scale linear programs Cited by: 6. Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem.

Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are by: 8. Although the max-norm can be computed in polynomial time, there are currently no practical algorithms for solving large-scale optimization problems that incorporate the max-norm.

Large-Scale Matrix Factorization with Distributed Stochastic Gradient Descent Rainer Gemulla1 Peter J. Haas 2Erik Nijkamp Yannis Sismanis 1Max-Planck-Institut fur Informatik¨ 2IBM Almaden Research Center Saarbrucken, Germany San Jose, CA, USA¨ [email protected] fphaas, enijkam, [email protected] Size: KB. Superfunctions and the Optimization of Large-Scale Dynamic Systems presents innovative perspectives on improving the performance of large scale systems affected by human control and provides an overview of how superfunctions enhance systems’ functionality.

Focusing on the foundations, design, and operation of superfunctions, this video is a. Many variants of batch NMF algorithms have been proposed in previous works to tackle large-scale data. They can be classified into three types, namely online NMF [17], [18], distributed NMF [ Large-scale Matrix Factorization (by Kijung Shin) 36/99 •Each step never increases, is updated to the “best” that minimizes.

Abstract We present modeling and solution strategies for large-scale resource allocation prob-lems that take place over multiple time periods under uncertainty.

In general, the strategies we present formulate the problem as a dynamic program and replace the value functions with tractable approximations.

The approximations of the value func. Optimization Methods for Large-Scale Machine Learning L eon Bottou Frank E. Curtisy Jorge Nocedalz J Abstract This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications.

Through case studiesFile Size: 1MB. The major goal of the book is to develop the theory of linear and integer linear optimization in a unified manner and then demonstrate how to use this theory in a modern computing environment to solve very large real world by: Dynamic Segmentation for Large-Scale Marketing Optimization into more fine-grained models that predict specific cus-tomer behaviors that must be aggregated to determine com-prehensive value and response models.

For instance, i’s response probability for hj;himay be decomposed into a channel propensity probability (i.e., probability iis reach-File Size: KB. Ro­bust coordinated optimization for large-scale dynamical systems. In: Pr. 4 IFAC/IFORS Symposium Large-Scale Systems: Theory and Applications.

Zurich, Author: Boris M. Mirkin, Nataly M. Lychenko. optimization problem turns out to be equivalent to dictio-nary learning. For small and medium sized datasets, with N. () An efficient variable interdependency-identification and decomposition by minimizing redundant computations for large-scale global optimization.

Information Sciences() Model reduction of dynamical systems on nonlinear manifolds using deep convolutional by: Approximate Dynamic Programming for Large-Scale Resource Allocation Problems Warren B. Powell tion; large-scale optimization 1. Introduction Many problems in operations research can be posed as managing a set of resources over mul-tiple time periods under uncertainty.

The resources may take on difierent forms in difierent. large-scale optimization, nonlinear programming, nonlinear inequality constraints, sequential quadratic programming, quasi-Newton methods, limited-memory methods AMS Subject Headings 49J20, 49J15, 49M37, 49D37, 65F05, 65K05, 90C30Cited by: when applied to large-scale systems.

The resulting algorithm is related to the reduced-gradient method of Wolfe [56] and the variable-reduction method of McCormick [41, 42]. It also draws much from the unconstrained and linearly- constrained optimization methods of Gill and Murray [21, 22, 25]. matrix factorization, and simpletouse.

Today’s challenges Develop sparse and stable(and invariant?) models. On large-scale optimization L. Bottou, F. Curtis and J. Nocedal. Optimization methods for large-scale machine learning, preprint arXiv, Y.

Nesterov. Introductory lectures on convex optimization: A basic. There is a growing need in major industries such as airline, trucking, financial engineering, etc. to solve very large linear and integer linear optimization problems. Because of the dramatic increase in computing power, it is now possible to solve these problems.

Along with the increase in computer power, the mathematical programming community has developed better and more powerful algorithms. tems, on large-scale problems; (4) more signi cantly, able to solve the largest matrix factorization problem ever reported.

This paper is organized as follows. Section 2 formulates the problem of matrix factorization and explains the two challenges in large-scale ALS, i.e., memory access on one GPU and scalability on multiple GPUs. Section 3. lar to [1]). In difference to other factorization methods that have also been applied to large scale datasets [2], it also utilizes closed-form solutions during optimization.

The pro-posed method is capable of factorizing hundreds of adjacency matrices of arbitrary shapes, that represent local closed-world. Setting up and solving a large optimization problem for portfolio optimization, constrained data fitting, parameter estimation, or other applications can be a challenging task.

As a result, it is common to first set up and solve a smaller, simpler version of the problem and then scale up to the large-scale problem. Book Chapters.

Mingyi Hong and Zhi-Quan Luo, “Signal Processing and Optimal Resource Allocation for the Interference Channel”, Academic Press Library in Signal Processing, Elsevier,available at. Mingyi Hong, Wei-Cheng Liao, Ruoyu Sun and Zhi-Quan Luo “Optimization Algorithms for Big Data with Application in Wireless Networks”, Big Data Over Networks, Cambridge University Press.

Outline. Section 2 formally de nes our optimization prob-lem and its distributed variant. We propose a synchronous algorithm in Section 3 and an asynchronous algorithm in Section 4.

Section 5 discusses large-scale graph partitioning and Section 6 details a novel approach to distribute parts of the graph over cluster nodes. Experiments on large File Size: 1MB. no practical algorithms for solving large-scale optimization problems that incor-porate the max-norm.

The present work uses a factorization technique of Burer and Monteiro [2] to devise scalable first-order algorithms for convex programs involving the max-norm. These algorithms are. Introduction and Problem Statement. Nonnegative matrix factorization (NMF) finds such nonnegative factors (matrices) A = [a ij] ∈ ℝ I×J and X = [x jt] ∈ ℝ J×T with a a ij ≥ 0, x jt ≥ 0 that Y ≅ AX, given the observation matrix Y = [y it] ∈ ℝ I×T, the lower-rank J, and possibly other statistical information on the observed data or the factors to be by: Large-scale optimization and decomposition methods: outline I Solution approaches for large-scaled problems: I Delayed column generation I Cutting plane methods (delayed constraint generation)7 I Problems amenable to the above methods: I Cutting stock problem, etc.

I Problems reformulated via decomposition methods I Benders decomposition I Dantzig-Wolfe decomposition. Current techniques for large-scale SfM from unordered photo collections (e.g, [1,11,21,25]) make heavy use of nonlinear optimization (bundle adjustment), which is sen-sitive to initialization.

Thus, these methods are run iter-atively, starting with a small set of photos, then repeat-edly adding photos and refining 3D points and camera poses. Dynamic factorization in large-scale optimization Mathematical Programming, Vol.

64, No. The practical conversion of linear programmes to network flow modelsCited by: LRSDP was proposed in [6] to efciently solve a large scale SDP [27].

In the following paragraphs, we briey dene the SDP and LRSDP problems, and discuss the efcient algorithm used for solving the LRSDP problem. SDP is a subeld of convex optimization concerned with the optimization of a linear objectiveCited by: A parallel contribution [3] considers matrix factorization as a framework for relational learning, with a focus on multiple relations (matrices) and large-scale optimization using stochastic approximations.

This paper, in contrast, focuses on modeling choices such as constraints, regularization, bias terms, and more. The simplest case of the gTF is factorization for a large-scale tensor partitioned into only two sub-tensors. If one sub-tensor is considered as a new data coming and expanding the current (actual) data along a single mode (usually time), the problem is referred to as the dynamic tensor analysis (DTA) or dynamic tensor factorization [3], [4].Cited by: introducing the low-rank factorization model () is thathopefully it is much faster to solve this model than model ().

However, there are two potential drawbacks of the low-rank factorization model (): (a) the non-convexity in the model may prevent one from getting a global solution, and (b) the approach requires an initial rank estimate K. Dynamic factorization in large-scale optimization Mathematical Programming, Vol.

64, No. A parametric programming methodology to solve the lagrangian dual Cited by: Stochastic Majorization-Minimization Algorithms for Large-Scale Optimization Julien Mairal To cite this version: factorization,or [9], which provides strongerguarantees, but for unconstrainedsmooth problems.

We develop several efficient algorithms based. Large Scale Matrix Factorization Fei Wang Division of Health Informatics Department of Healthcare Policy and Research Weill Cornell Medical College Cornell University 12/8/16 IEEE Big Data Conference 1.

Outline •Introduction •Matrix Factorization Technologies. UNESCO – EOLSS SAMPLE CHAPTERS OPTIMIZATION AND OPERATIONS RESEARCH – Vol.

II - Large-Scale Optimization - Alexander Martin ©Encyclopedia of Life Support Systems (EOLSS) 11 Ab A AxBBNN −−−∈] (3) we derive the Gomory cut, (see Combinatorial Optimization and Integer Programming) jj 0 jN f xf ∈ ∑ ≥ (4) It is valid for PI = conv{x ∈ n]+:Ax = b} and cuts off x.

Recently, a considerable growth of interest in projected gradient (PG) methods has been observed due to their high efficiency in solving large-scale convex minimization problems subject to linear constraints.

Since the minimization problems underlying nonnegative matrix factorization (NMF) of large matrices well matches this class of minimization problems, we investigate and test some recent Cited by:. torization for representing and predicting distances in large-scale networks. The essential idea is to approximate a large matrix whose elements represent pairwise distances by the product of two smaller matrices.

Such a model can be viewed as a form of dimensionality reduction. Models based on matrix factorization do not su er from the.Efficient Large-Scale Similarity Search Using Matrix Factorization 3 1 Introduction This paper is about image retrieval and similarity search for large datasets.

Image retrieval aims at finding the images in a large scale dataset most similar to a given query image. Recent approaches [16,23]Cited by: Matrix factorization Outline 1 Matrix factorization 2 Factorization machines 3 Field-aware factorization machines 4 Optimization methods for large-scale training 5 Discussion and conclusions Chih-Jen Lin (National Taiwan Univ.) 3 /