74 research outputs found
Optimization on Spheres: Models and Proximal Algorithms with Computational Performance Comparisons
No full textWe present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The common geometry binding these problems permits a generic application of algorithmic ideas and abstract convergence results for nonconvex optimization. We organize variational models for this problem into three different classes and derive the main algorithmic approaches within these classes (13 in all). We identify the central ideas underlying these methods and provide thorough numerical benchmarks comparing their performance on synthetic and laboratory data. The software and data of our experiments are all publicly accessible. We also introduce one new algorithm, a cyclic relaxed Douglas--Rachford algorithm, which outperforms all other algorithms by every measure: speed, stability, and accuracy. The analysis of this algorithm remains open
A simple globally convergent algorithm for the nonsmooth nonconvex single source localization problem
No full textProximal Heterogeneous Block Implicit-Explicit Method and Application to Blind Ptychographic Diffraction Imaging
No full textSemi-Bregman Proximal Alternating Method
No full textWe focus on nonconvex and non-smooth block optimization problems, where the smooth coupling part of the objective does not satisfy a global/partial Lipschitz gradient continuity assumption. A general alternating minimization algorithm is proposed that combines two proximal-based steps, one classical and another with respect to the Bregman divergence. Combining different analytical techniques, we provide a complete analysis of the behavior - from global to local - of the algorithm, and show when the iterates converge globally to critical points with a locally linear rate for sufficiently regular (though not necessarily convex) objectives. Numerical experiments illustrate the theoretical findings
Semi-Bregman Proximal Alternating Method
No full textWe focus on nonconvex and non-smooth block optimization problems, where the smooth coupling part of the objective does not satisfy a global/partial Lipschitz gradient continuity assumption. A general alternating minimization algorithm is proposed that combines two proximal-based steps, one classical and another with respect to the Bregman divergence. Combining different analytical techniques, we provide a complete analysis of the behavior - from global to local - of the algorithm, and show when the iterates converge globally to critical points with a locally linear rate for sufficiently regular (though not necessarily convex) objectives. Numerical experiments illustrate the theoretical findings
Semi-Bregman Proximal Alternating Method
No full textWe focus on nonconvex and non-smooth block optimization problems, where the smooth coupling part of the objective does not satisfy a global/partial Lipschitz gradient continuity assumption. A general alternating minimization algorithm is proposed that combines two proximal-based steps, one classical and another with respect to the Bregman divergence. Combining different analytical techniques, we provide a complete analysis of the behavior - from global to local - of the algorithm, and show when the iterates converge globally to critical points with a locally linear rate for sufficiently regular (though not necessarily convex) objectives. Numerical experiments illustrate the theoretical findings.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Israel Science Foundation http://dx.doi.org/10.13039/50110000397
A Framework for Globally Convergent Methods in Nonsmooth and Nonconvex Optimization
No full textNon UBCUnreviewedAuthor affiliation: Technion - Israel Institute of TechnologyResearche
Products of Finitely Many Resolvents of Maximal Monotone Mappings in Reflexive Banach Spaces
No full textPublisher Correction: Rapid volumetric optoacoustic imaging of neural dynamics across the mouse brain (Nature Biomedical Engineering, (2019), 3, 5, (392-401), 10.1038/s41551-019-0372-9).
No full textThe Author(s), under exclusive licence to Springer Nature Limited. In the HTML version of the Article originally published, Shy Shoham was mistakenly not denoted as a corresponding author; this has now been corrected. The PDF version was unaffected
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