SDPEN swMATH ID: 5152 Software Authors: G. Liuzzi, S. Lucidi, M. Sciandrone, K. Truemper Description: DFL - A Derivative-Free Library - SDPEN: Sequential penalty derivative-free methods for nonlinear constrained optimization. We consider the problem of minimizing a continuously differentiable function of several variables subject to smooth nonlinear constraints. We assume that the first order derivatives of the objective function and of the constraints can be neither calculated nor explicitly approximated. Hence, every minimization procedure must use only a suitable sampling of the problem functions. These problems arise in many industrial and scientific applications, and this motivates the increasing interest in studying derivative-free methods for their solution. The aim of the paper is to extend to a derivative-free context a sequential penalty approach for nonlinear programming. This approach consists in solving the original problem by a sequence of approximate minimizations of a merit function where penalization of constraint violation is progressively increased. In particular, under some standard assumptions, we introduce a general theoretical result regarding the connections between the sampling technique and the updating of the penalization which are able to guarantee convergence to stationary points of the constrained problem. On the basis of the general theoretical result, we propose a new method and prove its convergence to stationary points of the constrained problem. The computational behavior of the method has been evaluated both on a set of test problems and on a real application. The obtained results and the comparison with other well-known derivative-free software show the viability of the proposed sequential penalty approach. Homepage: http://www.iasi.cnr.it/~liuzzi/DFL/index.php/list3/10-local-optimization/6-sdpen Programming Languages: Fortran Keywords: derivative-free optimization; nonlinear programming; sequential penalty functions; numerical example; sampling technique; convergence Related Software: DFL; NOMAD; DFBOX_IMPR; SDBOX; DFLBOX; OrthoMADS; NEWUOA; DFN; MultiMin; DFLGEN; BOBYQA; DFO; APPSPACK; EGO; MCS; SNOBFIT; CUTEst; LCOBYQA; KELLEY; PSwarm Cited in: 23 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Sequential penalty derivative-free methods for nonlinear constrained optimization. Zbl 1223.65045Liuzzi, Giampaolo; Lucidi, Stefano; Sciandrone, Marco 2010 all top 5 Cited by 49 Authors 5 Lucidi, Stefano 4 Liuzzi, Giampaolo 4 Rinaldi, Francesco 2 Audet, Charles 2 Larson, Jeffrey 2 Sciandrone, Marco 2 Sun, Wenyu 2 Wild, Stefan M. 2 Xi, Min 1 Boukouvala, Fani 1 Bruni, Renato 1 Caporossi, Gilles 1 Celani, Fabio 1 Chen, Jun 1 Chen, Yannan 1 Conn, Andrew Roger 1 Cristofari, Andrea 1 Ehrhardt, Matthias Joachim 1 Floudas, Christodoulos Achilleus 1 Galvan, Giulio 1 Gao, Jing 1 Griffin, Joshua D. 1 Jacquet, Stéphane 1 Kolda, Tamara Gibson 1 Kvasov, Dmitriĭ Evgen’evich 1 Le Digabel, Sébastien 1 Lin, He 1 Lv, Wei 1 Maurici, Massimo 1 Menickelly, Matt 1 Misener, Ruth 1 Nuñez, Luigi 1 Paulon, Luca 1 Peyrega, Mathilde 1 Ploskas, Nikolaos 1 Quispel, Gilles Reinout Willem 1 Regis, Rommel G. 1 Riis, Erlend Skaldehaug 1 Roma, Massimo 1 Sahinidis, Nikolaos V. 1 Schönlieb, Carola-Bibiane 1 Sergeev, Yaroslav Dmitrievich 1 Sui, Ruirui 1 Sun, Hailin 1 Sun, Qiang 1 Tröltzsch, Anke 1 Truemper, Klaus 1 Varela, Kayla 1 Zhu, Detong all top 5 Cited in 16 Serials 3 Computational Optimization and Applications 3 Optimization Letters 2 Journal of Optimization Theory and Applications 2 Journal of Global Optimization 2 SIAM Journal on Optimization 1 Journal of Computational and Applied Mathematics 1 Operations Research Letters 1 European Journal of Operational Research 1 Computational and Applied Mathematics 1 Communications in Nonlinear Science and Numerical Simulation 1 Foundations of Computational Mathematics 1 Journal of Systems Science and Complexity 1 AMRX. Applied Mathematics Research eXpress 1 Acta Numerica 1 Mathematical Programming Computation 1 Numerical Algebra, Control and Optimization Cited in 5 Fields 23 Operations research, mathematical programming (90-XX) 4 Numerical analysis (65-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year