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. (Source:

References in zbMATH (referenced in 19 articles , 1 standard article )

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  1. Nikolovski, Filip; Stojkovska, Irena: Complex-step derivative approximation in noisy environment (2018)
  2. Bruni, Renato; Celani, Fabio: A robust optimization approach for magnetic spacecraft attitude stabilization (2017)
  3. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  4. Campana, Emilio F.; Diez, Matteo; Iemma, Umberto; Liuzzi, Giampaolo; Lucidi, Stefano; Rinaldi, Francesco; Serani, Andrea: Derivative-free global ship design optimization using global/local hybridization of the DIRECT algorithm (2016)
  5. Liuzzi, G.; Lucidi, S.; Piccialli, V.: Exploiting derivative-free local searches in DIRECT-type algorithms for global optimization (2016)
  6. Lucidi, Stefano; Maurici, Massimo; Paulon, Luca; Rinaldi, Francesco; Roma, Massimo: A derivative-free approach for a simulation-based optimization problem in healthcare (2016)
  7. Krejić, Nataša; Lužanin, Zorana; Nikolovski, Filip; Stojkovska, Irena: A nonmonotone line search method for noisy minimization (2015)
  8. Liuzzi, Giampaolo; Lucidi, Stefano; Rinaldi, Francesco: Derivative-free methods for mixed-integer constrained optimization problems (2015)
  9. Lv, Wei; Sun, Qiang; Lin, He; Sui, Ruirui: A penalty derivative-free algorithm for nonlinear constrained optimization (2015)
  10. Newby, Eric; Ali, M. M.: A trust-region-based derivative free algorithm for mixed integer programming (2015)
  11. Krejić, Nataša; Lužanin, Zorana; Stojkovska, Irena: A gradient method for unconstrained optimization in noisy environment (2013)
  12. Liuzzi, G.; Lucidi, S.; Rinaldi, F.: Derivative-free methods for bound constrained mixed-integer optimization (2012)
  13. Lewis, Robert Michael; Shepherd, Anne; Torczon, Virginia: Implementing generating set search methods for linearly constrained minimization (2007)
  14. Bagirov, Adil M.; Ghosh, Moumita; Webb, Dean: A derivative-free method for linearly constrained nonsmooth optimization (2006)
  15. Kolda, Tamara G.; Lewis, Robert Michael; Torczon, Virginia: Stationarity results for generating set search for linearly constrained optimization (2006)
  16. Kolda, Tamara G.: Revisiting asynchronous parallel pattern search for nonlinear optimization (2005)
  17. Kolda, Tamara G.; Lewis, Robert Michael; Torczon, Virginia: Optimization by direct search: New perspectives on some Classical and modern methods (2003)
  18. Lucidi, S.; Piccialli, V.: New classes of globally convexized filled functions for global optimization (2002)
  19. Lucidi, Stefano; Sciandrone, Marco: A derivative-free algorithm for bound constrained optimization (2002)