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

Jan Feiling, Mohamed Ali Belabbas, Christian Ebenbauer

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish (US)
Pages (from-to)6381-6396
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number12
StatePublished - Dec 1 2022


  • Adaptive control
  • extremum seeking
  • nonholonomic systems
  • optimization
  • optimization algorithms
  • perturbation methods

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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