UOBYQA: unconstrained optimization by quadratic approximation A new algorithm for general unconstrained optimization calculations is described. It takes account of the curvature of the objective function by forming quadratic models by interpolation. Obviously, no first derivatives are required. A typical iteration of the algorithm generates a new vector of variables either by minimizing the quadratic model subject to a trust region bound, or by a procedure that should improve the accuracy of the model. The paper addresses the initial positions of the interpolation points and the adjustment of trust region radii. par The algorithm works with the Lagrange functions of the interpolation equations explicitly; therefore their coefficients are updated when an interpolation point is moved. The Lagrange functions assist the procedure that improves the model and also they provide an estimate of the error of the quadratic approximation of the function being minimized. It is pointed out that results are very promising for functions with less than twenty variables.

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  1. Larson, Jeffrey; Billups, Stephen C.: Stochastic derivative-free optimization using a trust region framework (2016)
  2. Ni, Qin; Jiang, Cui; Liu, Hao: A new direct search method based on separable fractional interpolation model (2016)
  3. Wang, Jueyu; Zhu, Detong: Conjugate gradient path method without line search technique for derivative-free unconstrained optimization (2016)
  4. Ferreira, Priscila S.; Karas, Elizabeth W.; Sachine, Mael: A globally convergent trust-region algorithm for unconstrained derivative-free optimization (2015)
  5. Yuan, Ya-xiang: Recent advances in trust region algorithms (2015)
  6. Gumma, E.A.E.; Hashim, M.H.A.; Ali, M.Montaz: A derivative-free algorithm for linearly constrained optimization problems (2014)
  7. Zhang, Zaikun: Sobolev seminorm of quadratic functions with applications to derivative-free optimization (2014)
  8. Zhou, Qinghua; Geng, Yan: Revising two trust region subproblems for unconstrained derivative free methods (2014)
  9. Maxwell, Matthew S.; Henderson, Shane G.; Topaloglu, Huseyin: Tuning approximate dynamic programming policies for ambulance redeployment via direct search (2013)
  10. Regis, Rommel G.; Shoemaker, Christine A.: A quasi-multistart framework for global optimization of expensive functions using response surface models (2013)
  11. Rios, Luis Miguel; Sahinidis, Nikolaos V.: Derivative-free optimization: a review of algorithms and comparison of software implementations (2013)
  12. Zhao, Hui; Li, Gaoming; Reynolds, Albert C.; Yao, Jun: Large-scale history matching with quadratic interpolation models (2013)
  13. Arouxét, Ma.Belén; Echebest, Nélida; Pilotta, Elvio A.: Active-set strategy in Powell’s method for optimization without derivatives (2011)
  14. Luo, Changtong; Zhang, Shao-Liang; Wang, Chun; Jiang, Zonglin: A metamodel-assisted evolutionary algorithm for expensive optimization (2011)
  15. Regis, Rommel G.: Stochastic radial basis function algorithms for large-scale optimization involving expensive black-box objective and constraint functions (2011)
  16. Zhou, Qinghua; Li, Yan; Ha, Minghu: Constructing composite search directions with parameters in quadratic interpolation models (2011)
  17. Zhu, Jinghao; Zhou, Jiani; Gao, David: Global optimization by canonical dual function (2010)
  18. Deng, Geng; Ferris, Michael C.: Variable-number sample-path optimization (2009)
  19. Fasano, Giovanni; Morales, José Luis; Nocedal, Jorge: On the geometry phase in model-based algorithms for derivative-free optimization (2009)
  20. Gao, David Y.; Sherali, Hanif D.: Canonical duality theory: connections between nonconvex mechanics and global optimization (2009)

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