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Derivative-free optimization methods
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DOI：10.1017/S0962492919000060.png)
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Abstract
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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 high-lighting 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.
Keywords:
ADAPTIVE DIRECT SEARCH
TRUST-REGION METHODS
WORST-CASE COMPLEXITY
NELDER-MEAD ALGORITHM
EFFICIENT GLOBAL OPTIMIZATION
PARTIALLY SEPARABLE FUNCTIONS
IMPLICIT FILTERING ALGORITHM
BASIS FUNCTION INTERPOLATION
PARALLEL PATTERN SEARCH
MODEL-BASED ALGORITHMS
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