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.

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  1. Armstrong, Jerawan C.; Favorite, Jeffrey A.: Using a derivative-free optimization method for multiple solutions of inverse transport problems (2016)
  2. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  3. Csercsik, Dávid: Competition and cooperation in a bidding model of electrical energy trade (2016)
  4. Csercsik, Dávid: Lying generators: manipulability of centralized payoff mechanisms in electrical energy trade (2016)
  5. Fliege, Jörg; Vaz, A.Ismael F.: A method for constrained multiobjective optimization based on SQP techniques (2016)
  6. Lazar, Markus; Jarre, Florian: Calibration by optimization without using derivatives (2016)
  7. Paulavičius, Remigijus; Žilinskas, Julius: Advantages of simplicial partitioning for Lipschitz optimization problems with linear constraints (2016)
  8. Price, C.J.; Reale, M.; Robertson, B.L.: Stochastic filter methods for generally constrained global optimization (2016)
  9. Regis, Rommel G.: On the properties of positive spanning sets and positive bases (2016)
  10. Carvalho, Margarida; Pedroso, João Pedro; Saraiva, João: Electricity day-ahead markets: computation of Nash equilibria (2015)
  11. Custódio, A.L.; Madeira, J.F.A.: GLODS: global and local optimization using direct search (2015)
  12. Diouane, Y.; Gratton, S.; Vicente, L.N.: Globally convergent evolution strategies for constrained optimization (2015)
  13. Pourbagian, Mahdi; Talgorn, Bastien; Habashi, Wagdi G.; Kokkolaras, Michael; Le Digabel, Sébastien: Constrained problem formulations for power optimization of aircraft electro-thermal anti-icing systems (2015)
  14. Sinha, Pritibhushan: A method for solving some optimization problems with bounds on variables (2015)
  15. Sommer, A.; Farle, O.; Dyczij-Edlinger, R.: Certified dual-corrected radiation patterns of phased antenna arrays by offline-online order reduction of finite-element models (2015)
  16. Sommer, Alexander; Farle, Ortwin; Dyczij-Edlinger, Romanus: A fast certified parametric near-field-to-far-field transformation technique for electrically large antenna arrays (2015)
  17. Ceperic, Vladimir; Gielen, Georges; Baric, Adrijan: Sparse varepsilon $\varepsilon$-tube support vector regression by active learning (2014) ioport
  18. Domes, Ferenc; Fuchs, Martin; Schichl, Hermann; Neumaier, Arnold: The optimization test environment (2014)
  19. Le Thi, Hoai An; Huynh Van Ngai; Dinh, Tao Pham; Vaz, A.Ismael F.; Vicente, L.N.: Globally convergent DC trust-region methods (2014)
  20. Müller, Juliane; Shoemaker, Christine A.: Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems (2014)

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