DFN swMATH ID: 36998 Software Authors: G.Fasano, G.Liuzzi, S.Lucidi, F.Rinaldi, K. Truemper Description: DFL - A Derivative-Free Library - DFN: A linesearch-based derivative-free approach for nonsmooth constrained optimization. In this paper, we propose new linesearch-based methods for nonsmooth constrained optimization problems when first-order information on the problem functions is not available. In the first part, we describe a general framework for bound-constrained problems and analyze its convergence toward stationary points, using the Clarke–Jahn directional derivative. In the second part, we consider inequality constrained optimization problems where both objective function and constraints can possibly be nonsmooth. In this case, we first split the constraints into two subsets: difficult general nonlinear constraints and simple bound constraints on the variables. Then, we use an exact penalty function to tackle the difficult constraints and we prove that the original problem can be reformulated as the bound-constrained minimization of the proposed exact penalty function. Finally, we use the framework developed for the bound-constrained case to solve the penalized problem. Moreover, we prove that every accumulation point, under standard assumptions on the search directions, of the generated sequence of iterates is a stationary point of the original constrained problem. In the last part of the paper, we report extended numerical results on both bound-constrained and nonlinearly constrained problems, showing that our approach is promising when compared to some state-of-the-art codes from the literature. Homepage: http://www.iasi.cnr.it/~liuzzi/DFL/index.php/list3/13-nonsmooth-optimization-and-minimax-problems/14-dfn Dependencies: Fortran90; C Keywords: derivative-free optimization; Lipschitz optimization; exact penalty functions; inequality constrained optimization; stationarity conditions Related Software: DFL; OrthoMADS; NOMAD; SDPEN; DFBOX_IMPR; SDBOX; DGM; DIRECT; DFLBOX; BFO; MISO; KELLEY; GradSamp; PSwarm; PNEW; APPSPACK; DFLGEN; SO-I; BOBYQA; NEWUOA Cited in: 28 Documents Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Parallelized hybrid optimization methods for nonsmooth problems using NOMAD and linesearch. Zbl 1409.90190Liuzzi, G.; Truemper, K. 2018 A linesearch-based derivative-free approach for nonsmooth constrained optimization. Zbl 1302.90207Fasano, G.; Liuzzi, G.; Lucidi, S.; Rinaldi, F. 2014 all top 5 Cited by 53 Authors 9 Lucidi, Stefano 6 Liuzzi, Giampaolo 6 Rinaldi, Francesco 3 Santos, Sandra Augusta 2 Audet, Charles 2 Diniz-Ehrhardt, Maria Aparecida 2 Ferreira, Daniel Gil 2 Gaudioso, Manlio 2 Giallombardo, Giovanni 2 Larson, Jeffrey 2 Miglionico, Giovanna 2 Sciandrone, Marco 2 Wild, Stefan M. 1 Bagirov, Adil M. 1 Boukouvala, Fani 1 Bruni, Renato 1 Camponogara, Eduardo 1 Caporossi, Gilles 1 Celani, Fabio 1 Conn, Andrew Roger 1 Costa, M. Fernanda P. 1 De Santis, Alberto 1 Dellepiane, Umberto 1 DiPillo, Gianni 1 Ehrhardt, Matthias Joachim 1 Fasano, Giovanni 1 Fernandes, Edite M. G. P. 1 Floudas, Christodoulos Achilleus 1 Galvan, Giulio 1 García-Palomares, Ubaldo M. 1 Giovannelli, Tommaso 1 Giuliani, Caio Merlini 1 Graeb, Helmut E. 1 Habal, Husni 1 Helou, Elias Salomão 1 Jacquet, Stéphane 1 Kasimbeyli, Refail 1 Lapucci, Matteo 1 Latorre, Vittorio 1 Le Digabel, Sébastien 1 Levato, Tommaso 1 Menickelly, Matt 1 Misener, Ruth 1 Ozturk, Gurkan 1 Quispel, Gilles Reinout Willem 1 Renzi, Stefania 1 Riis, Erlend Skaldehaug 1 Rocha, Ana Maria A. C. 1 Saltet, Renaud 1 Schönlieb, Carola-Bibiane 1 Simões, Lucas Eduardo Azevedo 1 Truemper, Klaus 1 Vicente, Luis Nunes all top 5 Cited in 15 Serials 4 SIAM Journal on Optimization 4 Computational Optimization and Applications 3 Journal of Optimization Theory and Applications 3 Optimization Methods & Software 2 Computational and Applied Mathematics 2 Optimization Letters 2 Mathematical Programming Computation 1 Operations Research Letters 1 Annals of Operations Research 1 Journal of Global Optimization 1 European Journal of Operational Research 1 Top 1 Foundations of Computational Mathematics 1 4OR 1 Acta Numerica all top 5 Cited in 6 Fields 28 Operations research, mathematical programming (90-XX) 14 Numerical analysis (65-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year