OrthoMADS

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.


References in zbMATH (referenced in 62 articles )

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  1. Akimoto, Youhei; Auger, Anne; Glasmachers, Tobias; Morinaga, Daiki: Global linear convergence of evolution strategies on more than smooth strongly convex functions (2022)
  2. Giovannelli, Tommaso; Liuzzi, Giampaolo; Lucidi, Stefano; Rinaldi, Francesco: Derivative-free methods for mixed-integer nonsmooth constrained optimization (2022)
  3. Giuliani, Caio Merlini; Camponogara, Eduardo; Conn, Andrew R.: A derivative-free exact penalty algorithm: basic ideas, convergence theory and computational studies (2022)
  4. Ploskas, Nikolaos; Sahinidis, Nikolaos V.: Review and comparison of algorithms and software for mixed-integer derivative-free optimization (2022)
  5. Alarie, Stéphane; Audet, Charles; Bouchet, Pierre-Yves; Digabel, Sébastien Le: Optimization of stochastic blackboxes with adaptive precision (2021)
  6. Audet, Charles; Dzahini, Kwassi Joseph; Kokkolaras, Michael; Le Digabel, Sébastien: Stochastic mesh adaptive direct search for blackbox optimization using probabilistic estimates (2021)
  7. Bigeon, Jean; Le Digabel, Sébastien; Salomon, Ludovic: DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization (2021)
  8. Galvan, Giulio; Sciandrone, Marco; Lucidi, Stefano: A parameter-free unconstrained reformulation for nonsmooth problems with convex constraints (2021)
  9. Alimo, Ryan; Beyhaghi, Pooriya; Bewley, Thomas R.: Delaunay-based derivative-free optimization via global surrogates. III: nonconvex constraints (2020)
  10. Audet, Charles; Caporossi, Gilles; Jacquet, Stéphane: Binary, unrelaxable and hidden constraints in blackbox optimization (2020)
  11. Hare, Warren; Jarry-Bolduc, Gabriel: A deterministic algorithm to compute the cosine measure of a finite positive spanning set (2020)
  12. Hare, Warren; Planiden, Chayne; Sagastizábal, Claudia: A derivative-free (\mathcalV\mathcalU)-algorithm for convex finite-max problems (2020)
  13. Jarry-Bolduc, Gabriel; Nadeau, Patrick; Singh, Shambhavi: Uniform simplex of an arbitrary orientation (2020)
  14. Liuzzi, Giampaolo; Lucidi, Stefano; Rinaldi, Francesco: An algorithmic framework based on primitive directions and nonmonotone line searches for black-box optimization problems with integer variables (2020)
  15. Manno, Andrea; Amaldi, Edoardo; Casella, Francesco; Martelli, Emanuele: A local search method for costly black-box problems and its application to CSP plant start-up optimization refinement (2020)
  16. Verma, Aekaansh; Wong, Kwai; Marsden, Alison L.: A concurrent implementation of the surrogate management framework with application to cardiovascular shape optimization (2020)
  17. Audet, Charles; Côté-Massicotte, Julien: Dynamic improvements of static surrogates in direct search optimization (2019)
  18. Bei, Xiaoqiang; Zhu, Xiaoyan; Coit, David W.: A risk-averse stochastic program for integrated system design and preventive maintenance planning (2019)
  19. Bűrmen, Árpád; Fajfar, Iztok: Mesh adaptive direct search with simplicial Hessian update (2019)
  20. Larson, Jeffrey; Menickelly, Matt; Wild, Stefan M.: Derivative-free optimization methods (2019)

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