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 732 articles , 2 standard articles )

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  2. Chen, Haotian: On locating the zeros and poles of a meromorphic function (2022)
  3. Luo, Xin-long; Xiao, Hang; Lv, Jia-hui: Continuation Newton methods with the residual trust-region time-stepping scheme for nonlinear equations (2022)
  4. Martínez, J. M.; Santos, L. T.: On large-scale unconstrained optimization and arbitrary regularization (2022)
  5. Wang, Qifeng; Li, Weiguo; Bao, Wendi; Gao, Xingqi: Nonlinear Kaczmarz algorithms and their convergence (2022)
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  8. Amagai, Kenji; Hatano, Yuko; Machida, Manabu: Linear transport in porous media (2021)
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  10. Assunção, P. B.; Ferreira, O. P.; Prudente, L. F.: Conditional gradient method for multiobjective optimization (2021)
  11. Audet, Charles; Bigeon, Jean; Couderc, Romain: Combining cross-entropy and MADS methods for inequality constrained global optimization (2021)
  12. Awwal, Aliyu Muhammed; Mohammad, Hassan; Yahaya, Mahmoud Muhammad; Muhammadu, Ahmadu Bappah; Ishaku, Adamu: A new algorithm with structured diagonal Hessian approximation for solving nonlinear least squares problems and application to robotic motion control (2021)
  13. Birgin, E. G.; Martínez, J. M.; Ramos, A.: On constrained optimization with nonconvex regularization (2021)
  14. Braden, Jonathan; Burrage, Clare; Elder, Benjamin; Saadeh, Daniela: (\varphi)\textttenics: Vainshtein screening with the finite element method (2021)
  15. Dehghan Niri, T.; Heydari, M.; Hosseini, M. M.: An improvement of adaptive cubic regularization method for unconstrained optimization problems (2021)
  16. di Serafino, Daniela; Toraldo, Gerardo; Viola, Marco: Using gradient directions to get global convergence of Newton-type methods (2021)
  17. Fang, Minglei; Wang, Min; Sun, Min; Chen, Rong: A modified hybrid conjugate gradient method for unconstrained optimization (2021)
  18. Fischer, A.; Izmailov, A. F.; Solodov, M. V.: Accelerating convergence of the globalized Newton method to critical solutions of nonlinear equations (2021)
  19. Grapiglia, Geovani N.; Chorobura, Flávia: Worst-case evaluation complexity of derivative-free nonmonotone line search methods for solving nonlinear systems of equations (2021)
  20. Grapiglia, Geovani N.; Sachs, Ekkehard W.: A generalized worst-case complexity analysis for non-monotone line searches (2021)

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