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We implement the adaptive step size scheme from the optimization methods AdaGrad and Adam in a novel variant of the Proximal Gradient Method (PGM).
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Schmidt M, Roux NL, Bach FR (2011) Convergence rates of inexact Proximal-Gradient methods for convex optimization. In: Shawe-Taylor J, Zemel RS, Bartlett PL, Pereira F, Weinberger KQ (eds) Advances in Neural Information Processing Systems 24, Curran Associates, Inc., pp 1458–1466, URL http://papers.nips.cc/paper/4452-convergence-rates-of-inexact-proximal-gradient-methods-for-convex-optimization.pdf
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van der Walt S, Colbert SC, Varoquaux G (2011) The numpy array: A structure for efficient numerical computation. Computing in Science Engineering 13(2):22–30
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Melchior P, Moolekamp F, Jerdee M, Armstrong R, Sun AL, Bosch J, Lupton R (2018) scarlet: Source separation in multi-band images by constrained matrix factorization. Astronomy and Computing 24:129–142, DOI 10.1016/j.ascom.2018.07.001
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2013
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Chouzenoux E, Pesquet JC, Repetti A (2014) Variable metric forward–backward algorithm for minimizing the sum of a differentiable function and a convex function. Journal of optimization theory and applications 162(1):107–132, URL https://idp.springer.com/authorize/casa?redirect_uri=https://link.springer.com/article/10.1007/s10957-013-0465-7&casa_token=xvVjjzsKdiEAAAAA:tLQqDuveqsRZctMYOmpsLBDPf6Y96O_boGKVE3wtmWvZSsbfnIzXl4HMcCnz9gTWBoIZSaZmc7-GN6bR
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Parikh N, Boyd S (2014) Proximal algorithms. Foundations and Trends® in Optimization 1(3):127–239, DOI 10.1561/2400000003
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Reddi SJ, Kale S, Kumar S (2018) On the convergence of adam and beyond. URL https://openreview.net/pdf?id=ryQu7f-RZ
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Becker S, Fadili J, Ochs P (2019) On Quasi-Newton Forward-Backward splitting: Proximal calculus and convergence. SIAM journal on optimization: a publication of the Society for Industrial and Applied Mathematics pp 2445–2481, DOI 10.1137/18M1167152
2019
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Virtanen P, Gommers R, Oliphant TE, Haberland M, Reddy T, Cournapeau D, Burovski E, Peterson P, Weckesser W, Bright J, van der Walt SJ, Brett M, Wilson J, Jarrod Millman K, Mayorov N, Nelson ARJ, Jones E, Kern R, Larson E, Carey C, Polat İ, Feng Y, Moore EW, VanderPlas J, Laxalde D, Perktold J, Cimrman R, Henriksen I, Quintero EA, Harris CR, Archibald AM, Ribeiro AH, Pedregosa F, van Mulbregt P, Contributors S (2020) SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17:261–272, DOI https://doi.org/10.1038/s41592-019-0686-2
2020
Closest in time.