Related papers: Corrigendum to "Managerial Incentive Problems: A D…

This note serves two purposes. Firstly, we construct a counterexample to show that the statement on the convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex optimization problems in a…

We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…

Corrector estimates constitute a key ingredient in the derivation of optimal convergence rates via two-scale expansion techniques in homogenization theory of random uniformly elliptic equations. The present work follows up - in terms of…

This paper has been withdrawn by the author due to a crucial mistakes.

Recently, much work has been done on extending the scope of online learning and incremental stochastic optimization algorithms. In this paper we contribute to this effort in two ways: First, based on a new regret decomposition and a…

In the present article, we have given a corrigendum to our paper "Some approximation results on Bernstein-Schurer operators defined by (p,q)-integers" published in Journal of In- equalities and Applications (2015) 2015:249.

We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral…

In this note, the corrigendum to our earlier paper "Recover the source and initial value simultaneously in a parabolic equation" [2014 Inverse Problems 30 065013] is given.

For stochastic approximation algorithms with discontinuous dynamics, it is shown that under suitable distributional assumptions, the interpolated iterates track a Fillipov solution of the limiting differential inclusion. In addition, we…

The note corrects the aforementioned paper (also, arXiv:0902.4716). The consequences of the correction are traced and the examples updated.

The purpose of this erratum and addendum is to correct the errors in [1]. It consists of five components: 1. Lemma 7.1 and Proposition 7.2 are wrong and discarded; 2. A new proof of existence $\lambda(\xi)$ in (7.1) without Proposition 7.2;…

After the publication of [Compos. Math. 156 (2020), no. 4, 822-861], Andrew Putman pointed out a mistake in our paper and helped us fix it. In this note, we will explain what this mistake is and how to fix it.

Stochastic optimization methods have been hugely successful in making large-scale optimization problems feasible when computing the full gradient is computationally prohibitive. Using the theory of modified equations for numerical…

Inequalities for exponential sums are studied. Our results improve an old result of G. Halasz and a recent result of G. Kos. We prove several other essentially sharp related results in this paper.

This is erratum of the paper [Phys. Rev. Lett. {\bf 84}, 4260 (2000)]

We have fundamentally corrected the proofs of the theorems from our paper [9] by giving an entirely different approach, using quite a simple method based on applications of some elementary inequalities, well-known H\"older's inequality, and…

This paper has been withdrawn by the author due to errors.

In this paper, some points to the convergence analysis performed in the paper [A new computing approach for power signal modeling using fractional adaptive algorithms, ISA Transactions 68 (2017) 189-202] are presented. It is highlighted…

We prove that under five minimal axioms -- multi-dimensional quality, finite evaluation, effective optimization, resource finiteness, and combinatorial interaction -- any optimized AI agent will systematically under-invest effort in quality…

We provide a precise statement and self contained proof of a Sobolev inequality (cf. [A, page 236 and page 237]) stated in the original paper. Higher order and fractional inequalities are treated as well.