In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work studied approximate concerns coding schemes where replication factor is too low recover full exactly. Our motivated by challenge creating that simultaneously well in both adversarial and stochastic models. To e...

Semidefinite relaxations of certain combinatorial optimization problems lead to approximation algorithms with performance guarantees. For large-scale problems, it may not be computationally feasible to solve the semidefinite relaxations to optimality. In this paper, we investigate the effect on the performance guarantees of an approximate solution to the semidefinite relaxation for MaxCut, Max2...

The numerical solution of a large scale linear response eigenvalue problem is often accomplished by computing a pair of deflating subspaces associated with the interested part of the spectrum. This paper is concerned with the backward perturbation analysis for a given pair of approximate deflating subspaces or an approximate eigenquaternary. Various optimal backward perturbation bounds are obta...

We consider the problem of efficiently allocating simulation effort to determine which of several simulated systems have mean performance exceeding a known threshold. This determination is known as multiple comparisons with a control. Within a Bayesian formulation, the optimal fully sequential policy for allocating simulation effort is the solution to a dynamic program. We show that this dynami...

This paper presents a comparison between variational iteration method (VIM) and modfied variational iteration method (MVIM) for approximate solution a system of Volterra integral equation of the first kind. We convert a system of Volterra integral equations to a system of Volterra integro-di®erential equations that use VIM and MVIM to approximate solution of this system and hence obtain an appr...