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. 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)
  2. Beyhaghi, Pooriya; Bewley, Thomas R.: Delaunay-based derivative-free optimization via global surrogates. II: Convex constraints (2016)
  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. Audet, Charles; Le Digabel, Sébastien; Peyrega, Mathilde: Linear equalities in blackbox optimization (2015)
  5. Burmen, Árpád; Olenšek, Jernej; Tuma, Tadej: Mesh adaptive direct search with second directional derivative-based Hessian update (2015)
  6. Grippo, L.; Rinaldi, F.: A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations (2015)
  7. Adjengue, Luc; Audet, Charles; Ben Yahia, Imen: A variance-based method to rank input variables of the mesh adaptive direct search algorithm (2014)
  8. Alarie, Stéphane; Audet, Charles; Garnier, Vincent; Le Digabel, Sébastien; Leclaire, Louis-Alexandre: Snow water equivalent estimation using blackbox optimization (2013)
  9. Audet, C.; Dang, C.-K.; Orban, D.: Efficient use of parallelism in algorithmic parameter optimization applications (2013)
  10. Belitz, Paul; Bewley, Thomas: New horizons in sphere-packing theory, part II: Lattice-based derivative-free optimization via global surrogates (2013)
  11. Conn, Andrew R.; Le Digabel, Sébastien: Use of quadratic models with mesh-adaptive direct search for constrained black box optimization (2013)
  12. Rios, Luis Miguel; Sahinidis, Nikolaos V.: Derivative-free optimization: a review of algorithms and comparison of software implementations (2013)
  13. Stracquadanio, Giovanni; Romano, Vittorio; Nicosia, Giuseppe: Semiconductor device design using the BiMADS algorithm (2013)
  14. Van Dyke, Benjamin; Asaki, Thomas J.: Using QR decomposition to obtain a new instance of mesh adaptive direct search with uniformly distributed polling directions (2013)
  15. Audet, Charles; Le Digabel, Sébastien: The mesh adaptive direct search algorithm for periodic variables (2012)
  16. Stracquadanio, Giovanni; Pappalardo, Elisa; Pardalos, Panos M.: A mesh adaptive basin hopping method for the design of circular antenna arrays (2012)
  17. Audet, Charles; Dennis, J.E. jun.; Le Digabel, Sébastien: Globalization strategies for mesh adaptive direct search (2010)
  18. Audet, Charles; Fournier, Xavier; Hansen, Pierre; Messine, Frédéric: A note on diameters of point sets (2010)
  19. Audet, Charles; Savard, Gilles; Zghal, Walid: A mesh adaptive direct search algorithm for multiobjective optimization (2010)
  20. Kiwiel, Krzysztof C.: A nonderivative version of the gradient sampling algorithm for nonsmooth nonconvex optimization (2010)

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