![]() ![]() The algorithm, called Conjugate Gradient Hard Thresholding. This page collects recent research effort in this line. We propose a new iterative greedy algorithm to reconstruct sparse signals in Compressed Sensing. Proximal-Gradient Group Sparsity Proximal-Gradient for L1-Regularization Theproximal operatorforL1-regularizationwhen using step-size k, prox k kk 1 w k+1 2 2argmin v2Rd 1 2 kv wk+12 k2 + k kvk 1 involves solving asimple 1D problem for each variable j: wk+1 j 2argmin v j2R 1 2 (v j w k+1 2 j) 2 + k jv jj : The solution is given by. Exponentiated gradient 7 is a proximal algorithm to optimize over the probability simplex. ![]() with the goal of recovering a sparse vector under measurement noise. As a first application we consider recovering a sparse prob. We further consider an accelerated proximal gradient method 13 to speed. In this paper, we develop a proximal-gradient-subgradient algorithm with backtracked extrapolation (PGSABE) for solving problem (1.1). But many nonconvex problems of interest become amenable to simple and practical algorithms and rigorous analyses once the artificial separation is removed. sparse optimization, proximal gradient method, homotopy continuation. given in 25 to guarantee that L1-L2 can exactly recover a sparse vector. Specially, we consider sparse recovery with highly coherent matrices A, for which standard 1 regularization model usually fails. General nonconvex optimization is undoubtedly hard - in sharp contrast to convex optimization, of which there is good separation of problem structure, input data, and optimization algorithms. ![]()
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