We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures, yielding a O(d/T ) convergence rate for strongly convex objectives in d dimensions and O( √ s(log d)/T ) convergence rate when the optimum is s-sparse. Our algori...

Let {XN(t), t0}, N = 1,2,be a sequence of continuous-parameter Markov processes, and let T,(t)f(x)= EX[f(X,(t))]. Suppose that lim,NcT^(t)f(x)= T(t)f(x), and that convergence is uniform over x and over t E [0, K] for all K < o. When is convergence uniform over t E [0, oo)? Questions of this type are considered under the auxiliary condition that T(t)f(x) converges uniformly over x as t -> oo. A ...

in English: In 1985, Kyurkchiev and Andreev [1] constructed a sequence of iterative methods for finding all zeros of a polynomial simultaneously. In the literature there are only local convergence results for these methods (see [1, 5]). In this talk, we present a semilocal convergence theorem for Kyurkchiev-Andreev’s methods under computationally verifiable initial conditions and with an a post...

Influenced by Higham, Mao and Stuart [9], several numerical methods have been developed to study the strong convergence of the numerical solutions to stochastic differential equations (SDEs) under the local Lipschitz condition. These numerical methods include the tamed Euler–Maruyama (EM) method, the tamed Milstein method, the stopped EM, the backward EM, the backward forward EM, etc. Recently,...

Keywords: q-Bernstein–Schurer–Stancu operators q-integers Modulus of smoothness Rate of convergence a b s t r a c t In the present paper, we introduce the Stancu type generalization of the Bernstein–Schurer operators based on q integers. First, we prove the basic convergence of S ða;bÞ n;p ð:; q; xÞ and then obtain the rate of convergence by these operators in terms of the modulus of continuity...