Orthomads: A deterministic MADS instance with orthogonal directions The purpose of this paper is to introduce a new way of choosing directions for the mesh adaptive direct search (Mads) class of algorithms. The advantages of this new OrthoMads instantiation of Mads are that the polling directions are chosen deterministically, ensuring that the results of a given run are repeatable, and that they are orthogonal to each other, which yields convex cones of missed directions at each iteration that are minimal in a reasonable measure. Convergence results for OrthoMads follow directly from those already published for Mads, and they hold deterministically, rather than with probability one, as is the case for LtMads, the first Mads instance. The initial numerical results are quite good for both smooth and nonsmooth and constrained and unconstrained problems considered here.

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  1. Bei, Xiaoqiang; Zhu, Xiaoyan; Coit, David W.: A risk-averse stochastic program for integrated system design and preventive maintenance planning (2019)
  2. Audet, Charles; Ihaddadene, Amina; Le Digabel, Sébastien; Tribes, Christophe: Robust optimization of noisy blackbox problems using the mesh adaptive direct search algorithm (2018)
  3. Audet, Charles; Kokkolaras, Michael; Le Digabel, Sébastien; Talgorn, Bastien: Order-based error for managing ensembles of surrogates in mesh adaptive direct search (2018)
  4. Dreisigmeyer, David W.: Direct search methods on reductive homogeneous spaces (2018)
  5. Liuzzi, G.; Truemper, K.: Parallelized hybrid optimization methods for nonsmooth problems using NOMAD and linesearch (2018)
  6. Beyhaghi, Pooriya; Bewley, Thomas: Implementation of Cartesian grids to accelerate Delaunay-based derivative-free optimization (2017)
  7. Boukouvala, Fani; Faruque Hasan, M. M.; Floudas, Christodoulos A.: Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption (2017)
  8. Price, C. J.: A direct search quasi-Newton method for nonsmooth unconstrained optimization (2017)
  9. Armstrong, Jerawan C.; Favorite, Jeffrey A.: Using a derivative-free optimization method for multiple solutions of inverse transport problems (2016)
  10. Audet, Charles; Le Digabel, Sébastien; Tribes, Christophe: Dynamic scaling in the mesh adaptive direct search algorithm for blackbox optimization (2016)
  11. Beyhaghi, Pooriya; Bewley, Thomas R.: Delaunay-based derivative-free optimization via global surrogates. II: Convex constraints (2016)
  12. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  13. Gheribi, Aïmen E.; Harvey, Jean-Philippe; Bélisle, Eve; Robelin, Christian; Chartrand, Patrice; Pelton, Arthur D.; Bale, Christopher W.; Le Digabel, Sébastien: Use of a biobjective direct search algorithm in the process design of material science applications (2016)
  14. Regis, Rommel G.: On the properties of positive spanning sets and positive bases (2016)
  15. Audet, Charles; Le Digabel, Sébastien; Peyrega, Mathilde: Linear equalities in blackbox optimization (2015)
  16. Burmen, Árpád; Olenšek, Jernej; Tuma, Tadej: Mesh adaptive direct search with second directional derivative-based Hessian update (2015)
  17. Grippo, L.; Rinaldi, F.: A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations (2015)
  18. Adjengue, Luc; Audet, Charles; Ben Yahia, Imen: A variance-based method to rank input variables of the mesh adaptive direct search algorithm (2014)
  19. Ibrahim, Sharif; Sonnanburg, Kevin; Asaki, Thomas J.; Vixie, Kevin R.: Nonasymptotic densities for shape reconstruction (2014)
  20. Van Dyke, Benjamin: Equal angle distribution of polling directions in direct-search methods (2014)

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