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 courtesy of Gerhard Zumbusch

Confirmed Speakers & Participants

Workshop Schedule

Monday, September 29, 2014
TimeEventLocationMaterials
8:30 - 8:55Registration: Approximation, Integration, and Optimization Workshop11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45Exponential sums and tensor approximation - Wolfgang Dahmen, RWTH Aachen11th Floor Lecture Hall
9:55 - 10:40Adaptive Low-Rank Methods for High-Dimensional Second-Order Elliptic Problems - Markus Bachmayr, RWTH Aachen11th Floor Lecture Hall
10:50 - 11:10Coffee/Tea Break11th Floor Collaborative Space 
11:10 - 11:55Sparse Estimation with Strongly Correlated Variables - Robert D. Nowak, University of Wisconsin11th Floor Lecture Hall
12:05 - 1:50Break for lunch  
1:50 - 2:35Sparse, Adaptive Quadrature Methods for Bayesian Inverse Problems of Parametric Operator Equations - Christoph Schwab, ETH11th Floor Lecture Hall
2:45 - 3:30Distributed Optimization in Directed Graphs- Push-Sum Based Algorithms - Angelia Nedich, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
3:40 - 4:00Coffee/Tea Break11th Floor Lecture Hall 
4:00 - 4:45Estimating 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 - 6:30Welcome reception11th Floor Collaborative Space 
Tuesday, September 30, 2014
TimeEventLocationMaterials
9:00 - 9:45EIM, GEIM & Rectification - Yvon Maday, Brown University11th Floor Lecture Hall 
9:55 - 10:40A Quasi-Monte Carlo overview - Ian H. Sloan, The University of New South Wales11th Floor Lecture Hall
10:50 - 11:10Coffee/Tea Break11th Floor Collaborative Space 
11:10 - 11:55Application of quasi-Monte Carlo methods to PDEs with random coefficients - Frances Y. Kuo, University of New South Wales11th Floor Lecture Hall
12:05 - 1:50Break for lunch  
1:50 - 2:35Exponential Convergence and New Notions of Tractability for Analytic Multivariate Problems - Henryk Wozniakowski, Columbia University and University of Warsaw11th Floor Lecture Hall
2:45 - 3:30Complete Dictionary Recovery over the Sphere - John Wright, Columbia University11th Floor Lecture Hall 
3:40 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Compressive 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 - 9:45Exponential decay of reconstruction error from binary measurements of sparse signals - Simon Foucart, University of Georgia11th Floor Lecture Hall
9:55 - 10:40Maximum Likelihood Matrix Completion Under Sparse Factor Models- Error Guarantees and Efficient Algorithms - Jarvis Haupt, University of Minnesota11th Floor Lecture Hall
10:40 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:45High-Dimensionality Challenges in Uncertainty Quantification - Habib Najm, Sandia National Laboratories11th Floor Lecture Hall
11:50 - 12:00Group Photo11th Floor Lecture Hall 
12:00 - 1:30Break for lunch  
1:30 - 2:15Sparse structure-exploiting methods for large-scale Bayesian inverse problems - Omar Ghattas, University of Texas at Austin11th Floor Lecture Hall 
2:20 - 3:05Sparse regularization path by differential inclusion - Wotao Yin, University of California, Los Angeles11th Floor Lecture Hall
3:10 - 3:55Eigenvector 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 - 5:45Poster Session11th Floor Collaborative Space 
Thursday, October 2, 2014
TimeEventLocationMaterials
9:00 - 9:45Smoothing maximum functions - Michael Todd, Cornell University11th Floor Lecture Hall
9:55 - 10:40Convex relaxations for recovering simultaneously structured objects - Maryam Fazel, University of Washington11th Floor Lecture Hall
10:50 - 11:10Coffee/Tea Break11th Floor Collaborative Space 
11:10 - 11:55Nearly Linear-Time Algorithms for Structured Sparsity - Piotr Indyk, Massachusetts Institute of Technology11th Floor Lecture Hall
12:05 - 1:50Break for lunch  
1:50 - 2:35Compressive sensing approximation of high-dimensional parametric operator equations - Holger Rauhut, RWTH Aachen11th Floor Lecture Hall
2:45 - 3:30Streaming signal reconstruction from generalized measurements - Justin Romberg, Georgia Institute of Technology11th Floor Lecture Hall
3:40 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Relative Entropy Relaxations for Signomial Optimization - Venkat Chandrasekaran, California Institute of Technology11th Floor Lecture Hall
Friday, October 3, 2014
TimeEventLocationMaterials
8:55 - 9:40Adaptive low-rank approximations- a subspace point of view - Anthony Nouy, Ecole Centrale Nantes11th Floor Lecture Hall
10:00 - 10:45High-dimensional problems arising in molecular simulation - Eric Cances, Ecole Nationale des Ponts et Chaussees11th Floor Lecture Hall 
10:50 - 11:10Coffee/Tea Break11th Floor Collaborative Space 
11:10 - 11:55Completing any low-rank matrix, provably - Rachel Ward, University of Texas at Austin11th Floor Lecture Hall
12:05 - 1:50Break for lunch  
1:50 - 2:35Measure estimation from moments- from line spectra to tensors - Gongguo Tang, University of Wisconsin11th Floor Lecture Hall
2:45 - 3:30Nonlinear tensor product approximation - V.N. Temlyakov, University of South Carolina11th Floor Lecture Hall
3:40 - 4:00Coffee/Tea Break11th Floor Collaborative 

Associated Semester Workshops

High-dimensional Approximation
Discrepancy Theory

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