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 637 articles , 2 standard articles )

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  1. Cartis, Coralia; Gould, Nick I.; Toint, Philippe L.: Universal regularization methods: varying the power, the smoothness and the accuracy (2019)
  2. Chen, Ke; Grapiglia, Geovani Nunes; Yuan, Jinyun; Zhang, Daoping: Improved optimization methods for image registration problems (2019)
  3. Fan, Jinyan; Huang, Jianchao; Pan, Jianyu: An adaptive multi-step Levenberg-Marquardt method (2019)
  4. Gu, Ran; Yuan, Ya Xiang: A partial first-order affine-scaling method (2019)
  5. Amini, Keyvan; Rostami, Faramarz; Caristi, Giuseppe: An efficient Levenberg-Marquardt method with a new LM parameter for systems of nonlinear equations (2018)
  6. Audet, Charles; Tribes, Christophe: Mesh-based Nelder-Mead algorithm for inequality constrained optimization (2018)
  7. Baluch, Bakhtawar; Salleh, Zabidin; Alhawarat, Ahmad: A new modified three-term Hestenes-Stiefel conjugate gradient method with sufficient descent property and its global convergence (2018)
  8. Baumann, Manuel; Benner, Peter; Heiland, Jan: Space-time Galerkin POD with application in optimal control of semilinear partial differential equations (2018)
  9. Campos, Juan S.; Parpas, Panos: A multigrid approach to SDP relaxations of sparse polynomial optimization problems (2018)
  10. Cots, Olivier; Gergaud, Joseph; Goubinat, Damien: Direct and indirect methods in optimal control with state constraints and the climbing trajectory of an aircraft (2018)
  11. Dickstein, Flávio; Goldfeld, Paulo; Pfeiffer, Gustavo T.; Pinto, Renan V.: Truncated conjugate gradient and improved LBFGS and TSVD for history matching (2018)
  12. Dong, Li; Tang, Jingyong; Song, Xinyu: Numerical study of a smoothing algorithm for the complementarity system over the second-order cone (2018)
  13. Fang, Xiaowei; Ni, Qin; Zeng, Meilan: A modified quasi-Newton method for nonlinear equations (2018)
  14. Gonçalves, M. L. N.; Oliveira, F. R.: An inexact Newton-like conditional gradient method for constrained nonlinear systems (2018)
  15. Huang, Shuai; Wan, Zhong; Zhang, Jing: An extended nonmonotone line search technique for large-scale unconstrained optimization (2018)
  16. Kimiaei, Morteza: Nonmonotone self-adaptive Levenberg-Marquardt approach for solving systems of nonlinear equations (2018)
  17. Maggiar, Alvaro; Wächter, Andreas; Dolinskaya, Irina S.; Staum, Jeremy: A derivative-free trust-region algorithm for the optimization of functions smoothed via Gaussian convolution using adaptive multiple importance sampling (2018)
  18. Mohammad, Hassan; Santos, Sandra A.: A structured diagonal Hessian approximation method with evaluation complexity analysis for nonlinear least squares (2018)
  19. Nedělková, Zuzana; Lindroth, Peter; Patriksson, Michael; Strömberg, Ann-Brith: Efficient solution of many instances of a simulation-based optimization problem utilizing a partition of the decision space (2018)
  20. Nikolovski, Filip; Stojkovska, Irena: Complex-step derivative approximation in noisy environment (2018)

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