Scarcity in fossil fuel reserves and their environmental impacts has forced the world towards
the production of clean and environment-friendly fuels called biofuels. This review focuses …

Machine learning develops rapidly, which has made many theoretical breakthroughs and is
widely applied in various fields. Optimization, as an important part of machine learning, has …

In many optimization problems arising from scientific, engineering and artificial intelligence
applications, objective and constraint functions are available only as the output of a black …

In this paper, we analyze several methods for approximating gradients of noisy functions
using only function values. These methods include finite differences, linear interpolation …

The well-designed structures in neural networks reflect the prior knowledge incorporated
into the models. However, though different models have various priors, we are used to …

Three recent breakthroughs due to AI in arts and science serve as motivation: An award
winning digital image, protein folding, fast matrix multiplication. Many recent developments …

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 …

The goal of this paper is to investigate an approach for derivative-free optimization that has
not received sufficient attention in the literature and is yet one of the simplest to implement …

Abstract The late Professor MJD Powell devised five trust-region methods for derivative-free
optimization, namely COBYLA, UOBYQA, NEWUOA, BOBYQA, and LINCOA. He carefully …

We discuss two classes of methods of approximating gradients of noisy black box functions—
the classical finite difference method and recently popular randomized finite difference …