Abstract
We consider the problem of minimizing a function f subject to a single inequality constraint \(g(\mathbf x ) \le 0\), in a black-box scenario. We present a covariance matrix adaptation evolution strategy using an adaptive augmented Lagrangian method to handle the constraint. We show that our algorithm is an instance of a general framework that allows to build an adaptive constraint handling algorithm from a general randomized adaptive algorithm for unconstrained optimization. We assess the performance of our algorithm on a set of linearly constrained functions, including convex quadratic and ill-conditioned functions, and observe linear convergence to the optimum.
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References
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Acknowledgments
This work was supported by the grant ANR-2012-MONU-0009 (NumBBO) of the French National Research Agency.
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Atamna, A., Auger, A., Hansen, N. (2016). Augmented Lagrangian Constraint Handling for CMA-ES — Case of a Single Linear Constraint. In: Handl, J., Hart, E., Lewis, P., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds) Parallel Problem Solving from Nature – PPSN XIV. PPSN 2016. Lecture Notes in Computer Science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_17
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DOI: https://doi.org/10.1007/978-3-319-45823-6_17
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