PSwarm: a hybrid solver for linearly constrained global derivative-free optimization. PSwarm was developed originally for the global optimization of functions without derivatives and where the variables are within upper and lower bounds. The underlying algorithm used is a pattern search method, or more specifically, a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the (optional) search step of coordinate search, the algorithm incorporates a particle swarm scheme for dissemination of points in the feasible region, equipping the overall method with the capability of finding a global minimizer. Our extensive numerical experiments showed that the resulting algorithm is highly competitive with other global optimization methods based only on function values. PSwarm is extended in this paper to handle general linear constraints. The poll step now incorporates positive generators for the tangent cone of the approximated active constraints, including a provision for the degenerate case. The search step has also been adapted accordingly. In particular, the initial population for particle swarm used in the search step is computed by first inscribing an ellipsoid of maximum volume to the feasible set. We have again compared PSwarm with other solvers (including some designed for global optimization) and the results confirm its competitiveness in terms of efficiency and robustness.

References in zbMATH (referenced in 61 articles , 1 standard article )

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  1. Hare, Warren; Jarry-Bolduc, Gabriel: A deterministic algorithm to compute the cosine measure of a finite positive spanning set (2020)
  2. Sauk, Benjamin; Ploskas, Nikolaos; Sahinidis, Nikolaos: GPU parameter tuning for tall and skinny dense linear least squares problems (2020)
  3. Carbone, Maurizio; Iovieno, Michele: Application of the nonuniform fast Fourier transform to the direct numerical simulation of two-way coupled particle laden flows (2019)
  4. Ferreiro-Ferreiro, Ana M.; García-Rodríguez, José A.; Souto, Luis; Vázquez, Carlos: Basin hopping with synched multi L-BFGS local searches. Parallel implementation in multi-CPU and GPUs (2019)
  5. Gratton, S.; Royer, C. W.; Vicente, L. N.; Zhang, Z.: Direct search based on probabilistic feasible descent for bound and linearly constrained problems (2019)
  6. Liu, Jianfeng; Ploskas, Nikolaos; Sahinidis, Nikolaos V.: Tuning BARON using derivative-free optimization algorithms (2019)
  7. Sanguinetti, Guido (ed.); Huynh-Thu, Vân Anh (ed.): Gene regulatory networks. Methods and protocols (2019)
  8. Audet, Charles; Kokkolaras, Michael; Le Digabel, Sébastien; Talgorn, Bastien: Order-based error for managing ensembles of surrogates in mesh adaptive direct search (2018)
  9. Endres, Stefan C.; Sandrock, Carl; Focke, Walter W.: A simplicial homology algorithm for Lipschitz optimisation (2018)
  10. Gnandt, Christian; Callies, Rainer: CGRS -- an advanced hybrid method for global optimization of continuous functions closely coupling extended random search and conjugate gradient method (2018)
  11. Kieslich, Chris A.; Boukouvala, Fani; Floudas, Christodoulos A.: Optimization of black-box problems using Smolyak grids and polynomial approximations (2018)
  12. Larson, Jeffrey; Wild, Stefan M.: Asynchronously parallel optimization solver for finding multiple minima (2018)
  13. Le Thi, Hoai An; Pham Dinh, Tao: DC programming and DCA: thirty years of developments (2018)
  14. Beiranvand, Vahid; Hare, Warren; Lucet, Yves: Best practices for comparing optimization algorithms (2017)
  15. Feng, Quanxi; Liu, Sanyang; Zhang, Jianke; Yang, Guoping; Yong, Longquan: Improved biogeography-based optimization with random ring topology and Powell’s method (2017)
  16. Tran, Thi Thuy; Le Thi, Hoai An; Pham Dinh, Tao: DC programming and DCA for enhancing physical layer security via cooperative jamming (2017)
  17. Armstrong, Jerawan C.; Favorite, Jeffrey A.: Using a derivative-free optimization method for multiple solutions of inverse transport problems (2016)
  18. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  19. Csercsik, Dávid: Competition and cooperation in a bidding model of electrical energy trade (2016)
  20. Csercsik, Dávid: Lying generators: manipulability of centralized payoff mechanisms in electrical energy trade (2016)

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