Organizing Committee
Abstract

The workshop is devoted to the following problem of fundamental importance throughout science and engineering: how to approximate, integrate, or optimize multivariate functions.

The breakthroughs demanded by high dimensional problems may be at hand. Good methods of approximation arise as solutions of optimization problems over certain function classes that are now well understood in small and modesty large dimensions.

In high dimensions, the appropriate models involve sparse representations, which give rise to issues in nonlinear approximation methods such as greedy approximation. High dimensional optimization problems become intractable to solve exactly, but substantial gains in efficiency can be made by allowing for a small probability of failure (probabilistic recovery guarantees), and by seeking approximate solutions (up to a pre-specified threshold) rather than exact solutions. The contemporary requirements of numerical analysis connect approximation, optimization, and probabilistic analysis.

The workshop will bring together leading experts in approximation, compressed sensing and optimization.

Image for "Approximation, Integration, and Optimization"
Image courtesy of Gerhard Zumbusch

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, September 29, 2014
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration: Approximation, Integration, and Optimization Workshop11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45am EDTExponential sums and tensor approximation - Wolfgang Dahmen, RWTH Aachen11th Floor Lecture Hall
9:55 - 10:40am EDTAdaptive Low-Rank Methods for High-Dimensional Second-Order Elliptic Problems - Markus Bachmayr, RWTH Aachen11th Floor Lecture Hall
10:50 - 11:10am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:10 - 11:55am EDTSparse Estimation with Strongly Correlated Variables - Robert D. Nowak, University of Wisconsin11th Floor Lecture Hall
12:05 - 1:50pm EDTBreak for lunch  
1:50 - 2:35pm EDTSparse, Adaptive Quadrature Methods for Bayesian Inverse Problems of Parametric Operator Equations - Christoph Schwab, ETH11th Floor Lecture Hall
2:45 - 3:30pm EDTDistributed Optimization in Directed Graphs- Push-Sum Based Algorithms - Angelia Nedich, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
3:40 - 4:00pm EDTCoffee/Tea Break11th Floor Lecture Hall 
4:00 - 4:45pm EDTEstimating the n-width of solution manifolds of parametric PDE’s - Albert Cohen, Université de Paris VI (Pierre et Marie Curie)11th Floor Lecture Hall
4:55 - 6:30pm EDTWelcome reception11th Floor Collaborative Space 
Tuesday, September 30, 2014
TimeEventLocationMaterials
9:00 - 9:45am EDTEIM, GEIM & Rectification - Yvon Maday, Brown University11th Floor Lecture Hall 
9:55 - 10:40am EDTA Quasi-Monte Carlo overview - Ian H. Sloan, The University of New South Wales11th Floor Lecture Hall
10:50 - 11:10am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:10 - 11:55am EDTApplication of quasi-Monte Carlo methods to PDEs with random coefficients - Frances Y. Kuo, University of New South Wales11th Floor Lecture Hall
12:05 - 1:50pm EDTBreak for lunch  
1:50 - 2:35pm EDTExponential Convergence and New Notions of Tractability for Analytic Multivariate Problems - Henryk Wozniakowski, Columbia University and University of Warsaw11th Floor Lecture Hall
2:45 - 3:30pm EDTComplete Dictionary Recovery over the Sphere - John Wright, Columbia University11th Floor Lecture Hall 
3:40 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTCompressive Sampling of Sparse Polynomial Chaos Expansions- Convergence Analysis and Sampling Strategies - Alireza Doostan, University of Colorado11th Floor Lecture Hall
Wednesday, October 1, 2014
TimeEventLocationMaterials
9:00 - 9:45am EDTExponential decay of reconstruction error from binary measurements of sparse signals - Simon Foucart, University of Georgia11th Floor Lecture Hall
9:55 - 10:40am EDTMaximum Likelihood Matrix Completion Under Sparse Factor Models- Error Guarantees and Efficient Algorithms - Jarvis Haupt, University of Minnesota11th Floor Lecture Hall
10:40 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:45am EDTHigh-Dimensionality Challenges in Uncertainty Quantification - Habib Najm, Sandia National Laboratories11th Floor Lecture Hall
11:50 - 12:00pm EDTGroup Photo11th Floor Lecture Hall 
12:00 - 1:30pm EDTBreak for lunch  
1:30 - 2:15pm EDTSparse structure-exploiting methods for large-scale Bayesian inverse problems - Omar Ghattas, University of Texas at Austin11th Floor Lecture Hall 
2:20 - 3:05pm EDTSparse regularization path by differential inclusion - Wotao Yin, University of California, Los Angeles11th Floor Lecture Hall
3:10 - 3:55pm EDTEigenvector localization, implicit regularization, and algorithmic anti-differentiation for large-scale graphs and networked data - Michael W. Mahoney, University of California, Berkeley11th Floor Lecture Hall 
4:00 - 5:45pm EDTPoster Session11th Floor Collaborative Space 
Thursday, October 2, 2014
TimeEventLocationMaterials
9:00 - 9:45am EDTSmoothing maximum functions - Michael Todd, Cornell University11th Floor Lecture Hall
9:55 - 10:40am EDTConvex relaxations for recovering simultaneously structured objects - Maryam Fazel, University of Washington11th Floor Lecture Hall
10:50 - 11:10am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:10 - 11:55am EDTNearly Linear-Time Algorithms for Structured Sparsity - Piotr Indyk, Massachusetts Institute of Technology11th Floor Lecture Hall
12:05 - 1:50pm EDTBreak for lunch  
1:50 - 2:35pm EDTCompressive sensing approximation of high-dimensional parametric operator equations - Holger Rauhut, RWTH Aachen11th Floor Lecture Hall
2:45 - 3:30pm EDTStreaming signal reconstruction from generalized measurements - Justin Romberg, Georgia Institute of Technology11th Floor Lecture Hall
3:40 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTRelative Entropy Relaxations for Signomial Optimization - Venkat Chandrasekaran, California Institute of Technology11th Floor Lecture Hall
Friday, October 3, 2014
TimeEventLocationMaterials
8:55 - 9:40am EDTAdaptive low-rank approximations- a subspace point of view - Anthony Nouy, Ecole Centrale Nantes11th Floor Lecture Hall
10:00 - 10:45am EDTHigh-dimensional problems arising in molecular simulation - Eric Cances, Ecole Nationale des Ponts et Chaussees11th Floor Lecture Hall 
10:50 - 11:10am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:10 - 11:55am EDTCompleting any low-rank matrix, provably - Rachel Ward, University of Texas at Austin11th Floor Lecture Hall
12:05 - 1:50pm EDTBreak for lunch  
1:50 - 2:35pm EDTMeasure estimation from moments- from line spectra to tensors - Gongguo Tang, University of Wisconsin11th Floor Lecture Hall
2:45 - 3:30pm EDTNonlinear tensor product approximation - V.N. Temlyakov, University of South Carolina11th Floor Lecture Hall
3:40 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative 

Associated Semester Workshops

High-dimensional Approximation
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Discrepancy Theory
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Research Cluster

Lecture Videos

Nonlinear tensor product approximation

V.N. Temlyakov
University of South Carolina
October 3, 2014

Smoothing maximum functions

Michael Todd
Cornell University
October 2, 2014

A Quasi-Monte Carlo overview

Ian H. Sloan
The University of New South Wales
September 30, 2014

EIM, GEIM & Rectification

Yvon Maday
Brown University
September 30, 2014

Estimating the n-width of solution manifolds of parametric PDE's

Albert Cohen
Université de Paris VI (Pierre et Marie Curie)
September 29, 2014

Distributed Optimization in Directed Graphs- Push-Sum Based Algorithms

Angelia Nedich
University of Illinois at Urbana-Champaign
September 29, 2014