Derivative-free robust optimization by outer approximations

We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the a...

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Bibliographic Details
Published inMathematical programming Vol. 179; no. 1-2; pp. 157 - 193
Main Authors Menickelly, Matt, Wild, Stefan M.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2020
Springer Nature B.V
Springer
Subjects
Algorithms
Approximation
BASIC BIOLOGICAL SCIENCES
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Derivative-free optimization
Full Length Paper
Manifold sampling
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Minimax technique
Nonlinear programming
Numerical Analysis
Optimization
Outer approximation algorithms
Robust optimization
Robustness
Theoretical
Robust optimization
90C30
Outer approximation algorithms
90C47
Manifold sampling
90C56
65K10
Derivative-free optimization
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Summary:We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the algorithm output is established alongside desirable features of the model-based trust-region subproblems encountered. We demonstrate the practical benefits of the algorithm on a new class of test problems.
Bibliography:AC02-06CH11357
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-018-1326-9