OrthoMADS swMATH ID: 7713 Software Authors: Abramson, Mark A.; Audet, Charles; Dennis, J.E.jun.; Le Digabel, S'ebastien Description: 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. Homepage: http://www.caam.rice.edu/caam/trs/2008/TR08-03.pdf Keywords: mesh adaptive direct search (MADS) algorithms; deterministic; orthogonal directions; constrained optimization; nonlinear programming Related Software: NOMAD; DFL; MultiMin; DFN; EGO; SNOBFIT; IMFIL; NEWUOA; PSwarm; SDPEN; DFBOX_IMPR; SDBOX; ORBIT; BOBYQA; DFO; CUTEst; CUTEr; SifDec; DFLBOX; KELLEY Cited in: 64 Publications all top 5 Cited by 119 Authors 19 Audet, Charles 14 Le Digabel, Sébastien 5 Lucidi, Stefano 4 Bewley, Thomas R. 4 Dennis, John E. jun. 4 Liuzzi, Giampaolo 3 Asaki, Thomas J. 3 Beyhaghi, Pooriya 3 Marsden, Alison L. 3 Rinaldi, Francesco 3 Tribes, Christophe 2 Abramson, Mark A. 2 Alarie, Stéphane 2 Boukouvala, Fani 2 Bűrmen, Árpád 2 Conn, Andrew Roger 2 Floudas, Christodoulos Achilleus 2 Hare, Warren L. 2 Jarry-Bolduc, Gabriel 2 Kokkolaras, Michael 2 Sahinidis, Nikolaos V. 2 Sciandrone, Marco 2 Stracquadanio, Giovanni 2 Van Dyke, Benjamin 1 Adjengue, Luc D. 1 Akimoto, Youhei 1 Ali, Montaz M. 1 Alimo, Ryan 1 Armstrong, Jerawan C. 1 Auger, Anne 1 Bahrami, Salman 1 Bale, Christopher W. 1 Bei, Xiaoqiang 1 Bélisle, Eve 1 Belitz, Paul 1 Ben Yahia, Imen 1 Bigeon, Jean 1 Bouchet, Pierre-Yves 1 Camponogara, Eduardo 1 Caporossi, Gilles 1 Cartis, Coralia 1 Casella, Francesco 1 Chartrand, Patrice 1 Coit, David W. 1 Côté-Massicotte, Julien 1 Dang, C.-K. 1 Day, Marcus S. 1 Devals, Christophe 1 Dreisigmeyer, David W. 1 Dzahini, Kwassi Joseph 1 Fajfar, Iztok 1 Fanucchi, Dario 1 Faruque Hasan, M. M. 1 Favorite, Jeffrey A. 1 Feinstein, Jeffrey A. 1 Fournier, Xavier 1 Galvan, Giulio 1 Garnier, Vincent 1 Gheribi, Aïmen E. 1 Giovannelli, Tommaso 1 Giuliani, Caio Merlini 1 Glasmachers, Tobias 1 Graeb, Helmut E. 1 Grippo, Luigi 1 Guibault, François 1 Habal, Husni 1 Hansen, Pierre 1 Harvey, Jean-Philippe 1 Ibrahim, Sharif 1 Ihaddadene, Amina 1 Jacquet, Stéphane 1 Kiwiel, Krzysztof Czesław 1 Larson, Jeffrey 1 Latorre, Vittorio 1 Leclaire, Louis-Alexandre 1 Magallanez, Raymond jun. 1 Manno, Andrea 1 Martelli, Emanuele 1 Menickelly, Matt 1 Messine, Frédéric 1 Misener, Ruth 1 Morinaga, Daiki 1 Müller, Juliane 1 Nadeau, Patrick 1 Nicosia, Giuseppe 1 Olenšek, Jernej 1 Orban, Dominique 1 Pappalardo, Elisa 1 Pardalos, Panos M. 1 Pelton, Arthur D. 1 Peyrega, Mathilde 1 Phillips, Raymond 1 Planiden, Chayne 1 Ploskas, Nikolaos 1 Price, Christopher John 1 Regis, Rommel G. 1 Rios, Luis Miguel 1 Robelin, Christian 1 Roberts, Lindon 1 Romano, Vittorio ...and 19 more Authors all top 5 Cited in 23 Serials 10 Computational Optimization and Applications 8 Journal of Global Optimization 8 Optimization Letters 6 SIAM Journal on Optimization 6 Optimization and Engineering 3 Journal of Optimization Theory and Applications 3 European Journal of Operational Research 2 Journal of Computational Physics 2 Computational and Applied Mathematics 2 Optimization Methods & Software 2 Pacific Journal of Optimization 1 Computer Methods in Applied Mechanics and Engineering 1 Operations Research Letters 1 Optimization 1 Applied Mathematical Modelling 1 INFORMS Journal on Computing 1 Abstract and Applied Analysis 1 The ANZIAM Journal 1 Journal of Applied Mathematics 1 Structural and Multidisciplinary Optimization 1 Acta Numerica 1 Mathematical Programming Computation 1 Journal of Optimization all top 5 Cited in 13 Fields 61 Operations research, mathematical programming (90-XX) 19 Numerical analysis (65-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Statistics (62-XX) 2 Mechanics of deformable solids (74-XX) 2 Optics, electromagnetic theory (78-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Computer science (68-XX) 1 Fluid mechanics (76-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) Citations by Year