Gradient Approximation and Multivariable Derivative-Free Optimization Based on Noncommutative Maps

In this article, multivariable derivative-free optimization algorithms for unconstrained problems are developed. A novel procedure approximating the gradient of objective functions based on noncommutative maps is introduced. The construction an exploration sequence to specify where function evaluated and definition so-called generating which composed with function, such that mimics a descent algorithm. Various theoretical properties proposed class investigated numerical examples presented.