Sentence examples for proximal operator from inspiring English sources
On the other hand, the proposed model is difficult to solve due to its non-convexity and thus a new algorithm is developed to search one satisfying stationary solution through alternatively implementing one proximal operator operation and least-square fitting.
Then, the proximal operator is -Lipschitz continuous, that is, (2.23).
Then the proximal operator is defined as follows: (2.22).
The proximal operator (13) is sometimes called the block soft thresholding operator.
The proximal operator of g is defined by operatorname{prox}_{g}(x):=argmin _{yin H}biggl{ frac{ Vert y-x Vert ^{2}}{2}+g y biggr}, quad xin H. (8) The proximal operator of g of order (alpha>0) is defined as the proximal operator of αg.
The following lemmas (Lemma 2.3 and Lemma 2.4) describe the properties of the proximal operators.
In steps 7, 8 and 9, the proximal operators of the element-wise l1 norm, squared l2 norm, and column-wise group sparse regularizer are applied in sequence.
Furthermore, we assume that (f(x)) and (g y)) are 'simple' which means that their proximal operators have a closed-form representation or they can be efficiently solved up to a high precision [9].
The model is estimated with proximal operators to quickly discover a small number of key cell states and gene sets.
In our case, the multiple proximal operators do not provide a guaranteed convergence rate, but in practice, we find the accelerated gradient makes convergence significantly faster.
