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.

References in zbMATH (referenced in 24 articles , 2 standard articles )

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  1. Giovannelli, Tommaso; Liuzzi, Giampaolo; Lucidi, Stefano; Rinaldi, Francesco: Derivative-free methods for mixed-integer nonsmooth constrained optimization (2022)
  2. Giuliani, Caio Merlini; Camponogara, Eduardo; Conn, Andrew R.: A derivative-free exact penalty algorithm: basic ideas, convergence theory and computational studies (2022)
  3. De Santis, Alberto; Dellepiane, Umberto; Lucidi, Stefano; Renzi, Stefania: A derivative-free optimization approach for the autotuning of a forex trading strategy (2021)
  4. Galvan, Giulio; Sciandrone, Marco; Lucidi, Stefano: A parameter-free unconstrained reformulation for nonsmooth problems with convex constraints (2021)
  5. Lapucci, Matteo; Levato, Tommaso; Sciandrone, Marco: Convergent inexact penalty decomposition methods for cardinality-constrained problems (2021)
  6. Audet, Charles; Caporossi, Gilles; Jacquet, Stéphane: Binary, unrelaxable and hidden constraints in blackbox optimization (2020)
  7. Diniz-Ehrhardt, M. A.; Ferreira, D. G.; Santos, S. A.: Applying the pattern search implicit filtering algorithm for solving a noisy problem of parameter identification (2020)
  8. García-Palomares, Ubaldo M.: Non-monotone derivative-free algorithm for solving optimization models with linear constraints: extensions for solving nonlinearly constrained models via exact penalty methods (2020)
  9. Gaudioso, Manlio; Giallombardo, Giovanni; Miglionico, Giovanna: Essentials of numerical nonsmooth optimization (2020)
  10. Helou, Elias S.; Santos, Sandra A.; Simões, Lucas E. A.: A new sequential optimality condition for constrained nonsmooth optimization (2020)
  11. 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)
  12. Bagirov, A. M.; Ozturk, G.; Kasimbeyli, Refail: A sharp augmented Lagrangian-based method in constrained non-convex optimization (2019)
  13. Bruni, Renato; Celani, Fabio: Combining global and local strategies to optimize parameters in magnetic spacecraft control via attitude feedback (2019)
  14. Diniz-Ehrhardt, M. A.; Ferreira, D. G.; Santos, S. A.: A pattern search and implicit filtering algorithm for solving linearly constrained minimization problems with noisy objective functions (2019)
  15. Larson, Jeffrey; Menickelly, Matt; Wild, Stefan M.: Derivative-free optimization methods (2019)
  16. Latorre, Vittorio; Habal, Husni; Graeb, Helmut; Lucidi, Stefano: Derivative free methodologies for circuit worst case analysis (2019)
  17. Liuzzi, Giampaolo; Lucidi, Stefano; Rinaldi, Francesco; Vicente, Luis Nunes: Trust-region methods for the derivative-free optimization of nonsmooth black-box functions (2019)
  18. Costa, M. Fernanda P.; Rocha, Ana Maria A. C.; Fernandes, Edite M. G. P.: Filter-based DIRECT method for constrained global optimization (2018)
  19. Larson, Jeffrey; Wild, Stefan M.: Asynchronously parallel optimization solver for finding multiple minima (2018)
  20. Liuzzi, G.; Truemper, K.: Parallelized hybrid optimization methods for nonsmooth problems using NOMAD and linesearch (2018)

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