A note on the sufficient initial condition ensuring the convergence of directly extended 3-block ADMM for special semidefinite programming

The Growth of Entire Functions Defined by Laplace–Stieltjes Transforms Related to Proximate Order and Approximation

“…similar to the method in [1], and by using the Valiron-Knopp-Bohr formula, then it yields σ F u � +∞, that is, F(s) is an entire function in the whole plane. We denote L β to be a class of all the functions F(s) of form (1) which are analytic in the half plane Rs < β(− ∞ < β < ∞), and the sequence λ n satisfies (3) and (5), and denote L ∞ to be the class of all the functions F(s) of form (1) which are analytic in the whole plane Rs < +∞, and the sequence λ n satisfies (3), (5), and (4). us, if − ∞ < β <+∞ and F(s) ∈ L ∞ , then F(s) ∈ L β .…”

“…In 1963, Yu [1] first proved the Valiron-Knopp-Bohr formula of the associated abscissas of bounded convergence, absolute convergence, and uniform convergence of Laplace-Stieltjes transform when s � − z. Theorem 1. If the sequence λ n satisfies (3) and (5), then Laplace-Stieltjes transform (1) satisfies…”

The Growth on the Maximum Modulus of Double Dirichlet Series

“…For example, J. R. Yu, G. Srivastava, P. V. Filevich, Z. S. Gao, D. C. Sun, etc. studied the growth and value distribution of Dirichlet series and random Dirichlet series (see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]); Y. Y. Kong, G. T. Deng investigated the growth of Dirichlet-Hadamard product (see [18,19]); A. R. Reddy, M. N. Sheremeta, C. F. Yi, and H. Y. Xu studied the approximation of Dirichlet series (see [20][21][22][23][24]), and so on.…”

A three-operator splitting perspective of a three-block ADMM for convex quadratic semidefinite programming and extensions

“…In fact, many extensions and modifications of the classic ADMM of Glowinski and Marroco [11] and Gabay and Mercier [10] have been considered in recent years for solving the CQSDP problem via its dual, which is innately a 3-block separable convex optimization problem with one coupled linear constraint. Indeed, the most intuitive idea is to directly extend the classic ADMM to 3-block problems and the corresponding numerical performance is pretty good for many instances of problems [2,4,14,22]. However, the direct extension of ADMM (ADMMe) to problems with more than two blocks of variables is not guaranteed to be convergent (c.f.…”