Derivative-free optimization methods. (1st May 2019)

• Record Type: Journal Article
• Authors: Larson, Jeffrey; Menickelly, Matt; Wild, Stefan M.
• Is Part Of: Acta numerica. Volume 28(2019)
• Page Start: 287
• Page End: 404
• Publication Date: 2019-05-01
• Subjects: Numerical analysis -- Periodicals; 518
• DOI: 10.1017/S0962492919000060
• Languages: English
• ISSNs: 0962-4929

Abstract

Abstract : 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-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.