Notes on optimization software. This paper is an attempt to indicate the current state of optimization software and the search directions which should be considered in the near future. There are two parts of this paper. In the first part I discuss some of the issues that are relevant to the development of general optimization software. I have tried to focus on those issues which do not seem to have received sufficient attention and which would significantly benefit from further research. In addition, I have chosen issues that are particularly relevant to the development of software for optimization libraries. In the second part I illustrate some of the points raised in the first part by discussing algorithms for unconstrained optimization. Because the discussion in this part is brief, the interested reader may want to consult other papers in this volume for further information. In both parts my comments are influenced by my involvement in the MINPACK project and by my experiences in the development of MINPACK-1 [cf. the author, B. S. Garbow and K. E. Hillstrom, ACM Trans. Math. Software 7, 17-41 (1981; Zbl 0454.65049)]. (Source: http://plato.asu.edu)

References in zbMATH (referenced in 677 articles , 2 standard articles )

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  1. Bahrami, Somayeh; Amini, Keyvan: An efficient two-step trust-region algorithm for exactly determined consistent systems of nonlinear equations (2020)
  2. Boutet, Nicolas; Haelterman, Rob; Degroote, Joris: Secant update version of quasi-Newton PSB with weighted multisecant equations (2020)
  3. Gonçalves, Max L. N.; Menezes, Tiago C.: Gauss-Newton methods with approximate projections for solving constrained nonlinear least squares problems (2020)
  4. Gonçalves, M. L. N.; Oliveira, F. R.: On the global convergence of an inexact quasi-Newton conditional gradient method for constrained nonlinear systems (2020)
  5. Liu, Meixing; Ma, Guodong; Yin, Jianghua: Two new conjugate gradient methods for unconstrained optimization (2020)
  6. Marsland, Stephen; McLachlan, Robert I.; Wilkins, Matthew C.: Parallelization, initialization, and boundary treatments for the diamond scheme (2020)
  7. Ranocha, Hendrik; Sayyari, Mohammed; Dalcin, Lisandro; Parsani, Matteo; Ketcheson, David I.: Relaxation Runge-Kutta methods: fully discrete explicit entropy-stable schemes for the compressible Euler and Navier-Stokes equations (2020)
  8. Zhou, Weijun; Zhang, Li: A modified Broyden-like quasi-Newton method for nonlinear equations (2020)
  9. Ahookhosh, Masoud; Aragón Artacho, Francisco J.; Fleming, Ronan M. T.; Vuong, Phan T.: Local convergence of the Levenberg-Marquardt method under Hölder metric subregularity (2019)
  10. Audet, Charles; Le Digabel, Sébastien; Tribes, Christophe: The mesh adaptive direct search algorithm for granular and discrete variables (2019)
  11. Bao, Jifeng; Yu, Carisa Kwok Wai; Wang, Jinhua; Hu, Yaohua; Yao, Jen-Chih: Modified inexact Levenberg-Marquardt methods for solving nonlinear least squares problems (2019)
  12. Cartis, Coralia; Gould, Nick I.; Toint, Philippe L.: Universal regularization methods: varying the power, the smoothness and the accuracy (2019)
  13. Cartis, Coralia; Roberts, Lindon: A derivative-free Gauss-Newton method (2019)
  14. Chen, Ke; Grapiglia, Geovani Nunes; Yuan, Jinyun; Zhang, Daoping: Improved optimization methods for image registration problems (2019)
  15. Dong, Wen-Li; Li, Xing; Peng, Zheng: A simulated annealing-based Barzilai-Borwein gradient method for unconstrained optimization problems (2019)
  16. Fajfar, Iztok; Bűrmen, Árpád; Puhan, Janez: The Nelder-Mead simplex algorithm with perturbed centroid for high-dimensional function optimization (2019)
  17. Fan, Jinyan; Huang, Jianchao; Pan, Jianyu: An adaptive multi-step Levenberg-Marquardt method (2019)
  18. Gu, Ran; Yuan, Ya Xiang: A partial first-order affine-scaling method (2019)
  19. Kimiaei, Morteza; Rahpeymaii, Farzad: A new nonmonotone line-search trust-region approach for nonlinear systems (2019)
  20. Mita, Kanako; Fukuda, Ellen H.; Yamashita, Nobuo: Nonmonotone line searches for unconstrained multiobjective optimization problems (2019)

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