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 701 articles , 2 standard articles )

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  1. Birgin, E. G.; Martínez, J. M.; Ramos, A.: On constrained optimization with nonconvex regularization (2021)
  2. Fischer, A.; Izmailov, A. F.; Solodov, M. V.: Accelerating convergence of the globalized Newton method to critical solutions of nonlinear equations (2021)
  3. Hansen, Nikolaus; Auger, Anne; Ros, Raymond; Mersmann, Olaf; Tušar, Tea; Brockhoff, Dimo: COCO: a platform for comparing continuous optimizers in a black-box setting (2021)
  4. Price, C. J.; Reale, M.; Robertson, B. L.: \textscOscars-II: an algorithm for bound constrained global optimization (2021)
  5. Bahrami, Somayeh; Amini, Keyvan: An efficient two-step trust-region algorithm for exactly determined consistent systems of nonlinear equations (2020)
  6. Bergou, El Houcine; Diouane, Youssef; Kungurtsev, Vyacheslav: Convergence and complexity analysis of a Levenberg-Marquardt algorithm for inverse problems (2020)
  7. Bergou, El Houcine; Gorbunov, Eduard; Richtárik, Peter: Stochastic three points method for unconstrained smooth minimization (2020)
  8. Birgin, E. G.; Gardenghi, J. L.; Martínez, J. M.; Santos, S. A.: On the use of third-order models with fourth-order regularization for unconstrained optimization (2020)
  9. Boutet, Nicolas; Haelterman, Rob; Degroote, Joris: Secant update version of quasi-Newton PSB with weighted multisecant equations (2020)
  10. Chen, Liang; Ma, Yanfang: Shamanskii-like Levenberg-Marquardt method with a new line search for systems of nonlinear equations (2020)
  11. Costa, Carina Moreira; Grapiglia, Geovani Nunes: A subspace version of the Wang-Yuan augmented Lagrangian-trust region method for equality constrained optimization (2020)
  12. Freno, Brian A.; Johnson, William A.; Zinser, Brian F.; Campione, Salvatore: Symmetric triangle quadrature rules for arbitrary functions (2020)
  13. Golman, Boris; Andreev, Vsevolod V.; Skrzypacz, Piotr: Dead-core solutions for slightly non-isothermal diffusion-reaction problems with power-law kinetics (2020)
  14. Gonçalves, Max L. N.; Menezes, Tiago C.: Gauss-Newton methods with approximate projections for solving constrained nonlinear least squares problems (2020)
  15. Gonçalves, M. L. N.; Oliveira, F. R.: On the global convergence of an inexact quasi-Newton conditional gradient method for constrained nonlinear systems (2020)
  16. Gonçalves, M. L. N.; Prudente, L. F.: On the extension of the Hager-Zhang conjugate gradient method for vector optimization (2020)
  17. Gratton, S.; Toint, Ph. L.: A note on solving nonlinear optimization problems in variable precision (2020)
  18. Hare, Warren; Jarry-Bolduc, Gabriel: Calculus identities for generalized simplex gradients: rules and applications (2020)
  19. Hassan, Basim A.: A new type of quasi-Newton updating formulas based on the new quasi-Newton equation (2020)
  20. Li, Pengyuan; Wang, Zhan; Luo, Dan; Pham, Hongtruong: Global convergence of a modified two-parameter scaled BFGS method with Yuan-Wei-Lu line search for unconstrained optimization (2020)

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