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A derivative-free algorithm for bound constrained optimization We propose a new globally convergent derivative-free algorithm for the minimization of a continuously differentiable function in the case that some of (or all) the variables are bounded. This algorithm investigates the local behaviour of the objective function on the feasible set by sampling it along the coordinate directions. Whenever a “suitable” descent feasible coordinate direction is detected a new point is produced by performing a linesearch along this direction. The information progressively obtained during the iterates of the algorithm can be used to build an approximation model of the objective function. The minimum of such a model is accepted if it produces an improvement of the objective function value. We also derive a bound for the limit accuracy of the algorithm in the minimization of noisy functions. Finally, we report the results of a preliminary numerical experience.
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References in zbMATH (referenced in 26 articles , 1 standard article )
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Sorted by year (- Paradezhenko, G. V.; Melnikov, N. B.; Reser, B. I.: Numerical continuation method for nonlinear system of scalar and functional equations (2020)
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- Gratton, S.; Royer, C. W.; Vicente, L. N.; Zhang, Z.: Direct search based on probabilistic feasible descent for bound and linearly constrained problems (2019)
- Larson, Jeffrey; Menickelly, Matt; Wild, Stefan M.: Derivative-free optimization methods (2019)
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- Nikolovski, Filip; Stojkovska, Irena: Complex-step derivative approximation in noisy environment (2018)
- Bruni, Renato; Celani, Fabio: A robust optimization approach for magnetic spacecraft attitude stabilization (2017)
- Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
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- Krejić, Nataša; Lužanin, Zorana; Nikolovski, Filip; Stojkovska, Irena: A nonmonotone line search method for noisy minimization (2015)
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- Newby, Eric; Ali, M. M.: A trust-region-based derivative free algorithm for mixed integer programming (2015)
- Krejić, Nataša; Lužanin, Zorana; Stojkovska, Irena: A gradient method for unconstrained optimization in noisy environment (2013)
- Liuzzi, G.; Lucidi, S.; Rinaldi, F.: Derivative-free methods for bound constrained mixed-integer optimization (2012)
- Lewis, Robert Michael; Shepherd, Anne; Torczon, Virginia: Implementing generating set search methods for linearly constrained minimization (2007)