DFL - A Derivative-Free Library - DFMO: A derivative-free approach to constrained multiobjective nonsmooth optimization. In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. We define a linesearch-based solution method, and we show that it converges to a set of Pareto stationary points. To this aim, we carry out a theoretical analysis of the problem by only assuming Lipschitz continuity of the functions; more specifically, we give new optimality conditions that take explicitly into account the bound constraints, and prove that the original problem is equivalent to a bound constrained problem obtained by penalizing the nonlinear constraints with an exact merit function. Finally, we present the results of some numerical experiments on bound constrained and nonlinearly constrained problems, showing that our approach is promising when compared to a state-of-the-art method from the literature.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Assunção, P. B.; Ferreira, O. P.; Prudente, L. F.: Conditional gradient method for multiobjective optimization (2021)
  2. Audet, Charles; Bigeon, Jean; Cartier, Dominique; Le Digabel, Sébastien; Salomon, Ludovic: Performance indicators in multiobjective optimization (2021)
  3. Bigeon, Jean; Le Digabel, Sébastien; Salomon, Ludovic: DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization (2021)
  4. Custódio, Ana Luísa; Diouane, Youssef; Garmanjani, Rohollah; Riccietti, Elisa: Worst-case complexity bounds of directional direct-search methods for multiobjective optimization (2021)
  5. Brás, C. P.; Custódio, A. L.: On the use of polynomial models in multiobjective directional direct search (2020)
  6. Cocchi, G.; Lapucci, M.: An augmented Lagrangian algorithm for multi-objective optimization (2020)
  7. Cocchi, G.; Liuzzi, G.; Lucidi, S.; Sciandrone, M.: On the convergence of steepest descent methods for multiobjective optimization (2020)
  8. Cocchi, Guido; Levato, Tommaso; Liuzzi, Giampaolo; Sciandrone, Marco: A concave optimization-based approach for sparse multiobjective programming (2020)
  9. Larson, Jeffrey; Menickelly, Matt; Wild, Stefan M.: Derivative-free optimization methods (2019)
  10. Wang, Peng; Zhu, Detong; Song, Yufeng: Derivative-free feasible backtracking search methods for nonlinear multiobjective optimization with simple boundary constraint (2019)
  11. Campana, E. F.; Diez, M.; Liuzzi, G.; Lucidi, S.; Pellegrini, R.; Piccialli, V.; Rinaldi, F.; Serani, A.: A multi-objective \textbfDIRECTalgorithm for ship hull optimization (2018)
  12. Cocchi, G.; Liuzzi, G.; Papini, A.; Sciandrone, M.: An implicit filtering algorithm for derivative-free multiobjective optimization with box constraints (2018)
  13. Custódio, A. L.; Madeira, J. F. A.: MultiGLODS: global and local multiobjective optimization using direct search (2018)
  14. Liuzzi, G.; Lucidi, S.; Rinaldi, F.: A derivative-free approach to constrained multiobjective nonsmooth optimization (2016)