Erratum: Hoffman's Error Bound, Local Controllability, and Sensitivity Analysis

Notes on Local Controllability

The first part of these notes is a motivating example which justifies, apart from pure intellectual curiosity, our desire to delve into the details of Sussmann’s local controllability results presented in [2]. The following sections then summarize various results in the paper. Possibly the hardest part of reading Sussmann’s paper is keeping track of all the notation. The Appendix presents a lis...

Control Variations and Local Controllability

Adaptive refinement for a local error bound based on duality

This paper presents the basis of an adaptive mesh refinement technique aimed at reducing a local error, i.e. the error in a local quantity, which is defined as the integral of a stress or a displacement in a given subregion. Two pairs of dual solutions, one corresponding to the applied load and the other to the virtual action, dual of the local quantity, are used to bound the local error and to...

Accelerate Stochastic Subgradient Method by Leveraging Local Error Bound

In this paper, we propose two accelerated stochastic subgradient methods for stochastic non-strongly convex optimization problems by leveraging a generic local error bound condition. The novelty of the proposed methods lies at smartly leveraging the recent historical solution to tackle the variance in the stochastic subgradient. The key idea of both methods is to iteratively solve the original ...

Root Cause and Error Analysis

Error is an inevitable part of life and cannot be completely eliminated, but it can be minimized. A root cause analysis is a technique for understanding the systematic error causes that is involved beyond a person or people to implement an errors and including field and environmental causes of errors when occur in this situation too. An important factor of an error occurrence is a root cause (c...