Interdisciplinary Workshop on Fixed-Point Algorithms for Inverse Problems in Science and Engineering (09w5006)

Arriving in Banff, Alberta Sunday, November 1 and departing Friday November 6, 2009

Organizers

(University of British Columbia)

(University of South Australia)

(North Carolina State University)

(Cornell University)

Russell Luke (University of Delaware)

(University of Waterloo)

Objectives

Our objective is to bring together researchers
with a strong interest in projection and other first-order fixed-point algorithms, both from mathematics and from the applied sciences, in order to survey the state-of-the-art of theory and practice, to identify emerging problems driven by applications, and to discuss new approaches for solving these problems.

The proposed workshop is timely and unique. Monographs and conference proceedings on projection methods and their applications have been published very recently, see the list of references below. The proposed group of world-class participants has not met before and is very unlikely to meet at ordinary optimization conferences. We expect this workshop to be the base for new innovative research and collaborations by mixing experts whose areas of applications are broad, ranging from variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics and chemistry.

Fueled by this workshop, we expect research contributions on newly emerging links between first-order fixed-point algorithms
and applications.

Topics of the proposed workshop include:

* Theory of fixed-point algorithms:
convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis,
proximal point methods, projection methods,
resolvent and related fixed-point theoretic methods, and monotone operator theory.

* Numerical analysis of fixed-point algorithms:
choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of
ill-posed problems; numerical comparison of various methods.

* Areas of Applications:
engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas.

[B97] C. Brezinski: Projections Methods for Systems of Equations, North Holland, 1997.

[BCR01] D. Butnariu, Y. Censor, and S. Reich:
Inherently Parallel Algorithms in Feasibility and
Optimization and their Applications, North Holland, 2001.

[CR07] E.J. Candes and J. Romberg: Sparsity and incoherence in compressive sampling, Inverse Problems 2:969-986, 2007.

[CZ97] Y. Censor and S. Zenios: Parallel Optimization, Oxford, 1997.

[CW05] P.L. Combettes and V.R. Wajs: Signal recovery by proximal forward-backward splitting,
SIAM Journal on Multiscale Modeling and Simulation 4:1168-1200, 2005.

[Da06] J. Dattorro: Convex Optimization & Euclidean Distance Geometry, Lulu, 2006.

[De01] F. Deutsch: Best Approximation in Inner Product Spaces, Springer, 2001.

[Do06] D. Donoho: Compressed sensing,
IEEE Transactions on Information Theory 52:1289-1306, 2006.

[ERT07] V. Elser, I. Rankenburg, and P. Thibault:
Searching with iterated maps, Proceedings of the National Academy of Sciences USA 104, 2007.

[G03] A. Galantai: Projectors and Projection Methods, Springer, 2003.

[H02] N.J. Higham: Computing the nearest correlation matrix - a problem from finance,
IMA Journal of Numerical Analysis 22:329-343, 2002.

[L02] D.R. Luke, J.V. Burke, and R.G. Lyon:
Optical wavefront reconstruction: Theory and numerical methods, SIAM Review 44:169-224, 2002.

[L05] D.R. Luke: Relaxed averaged alternating reflections for diffraction imaging, Inverse Problems 21:37-50, 2005.

[LM] L.M. Marks and D.R. Luke: Robust Mixing for Ab-Initio DFT Calculations, in preparation.

[M07] S. Marchesini: A unified evaluation of iterative projection algorithms for phase retrieval, Review of Scientific Instrumentation 78, 2007.

[RCT05] J. Romberg, E.J. Candes, and T. Tao:
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory 52:489-509, 2005.

[SlY07] K. Slavakis and I. Yamada: Robust wideband beamforming by the hybrid steepest descent method,
IEEE Transactions on Signal Processing 55:4511-4522, 2007.

[StY98] H. Stark and Y. Yang: Vector Space Projections, Wiley, 1998.

[TEJSS06] P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre: Reconstruction of a yeast cell from X-ray diffraction data, Acta Crystallographica A62: 248-261, 2006