7 citations · 14 across the 5 of their papers we have counts for
6 papers
The Error in Multivariate Linear Extrapolation with Applications to Derivative-Free Optimization
Liyuan Cao, Zaiwen Wen, Ya-xiang Yuan
We study in this paper the function approximation error of multivariate linear extrapolation. The sharp error bound of linear interpolation already exists in the literature. Howeve…
Some Sharp Error Bounds for Multivariate Linear Interpolation and Extrapolation
Liyuan Cao, Zaiwen Wen, Ya-xiang Yuan
We study in this paper the function approximation error of linear interpolation and extrapolation. Several upper bounds are presented along with the conditions under which they are…
First- and Second-Order High Probability Complexity Bounds for Trust-Region Methods with Noisy Oracles
Liyuan Cao, Albert S. Berahas, Katya Scheinberg
In this paper, we present convergence guarantees for a modified trust-region method designed for minimizing objective functions whose value and gradient and Hessian estimates are c…
Global Convergence Rate Analysis of a Generic Line Search Algorithm with Noise
Albert S. Berahas, Liyuan Cao, Katya Scheinberg
In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and whose gradient estimates are inexact…
Linear interpolation gives better gradients than Gaussian smoothing in derivative-free optimization
Albert S Berahas, Liyuan Cao, Krzysztof Choromanski +1
In this paper, we consider derivative free optimization problems, where the objective function is smooth but is computed with some amount of noise, the function evaluations are exp…
A Theoretical and Empirical Comparison of Gradient Approximations in Derivative-Free Optimization
Albert S. Berahas, Liyuan Cao, Krzysztof Choromanski +1
In this paper, we analyze several methods for approximating gradients of noisy functions using only function values. These methods include finite differences, linear interpolation,…