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 580 articles , 2 standard articles )

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  1. Campos, Juan S.; Parpas, Panos: A multigrid approach to SDP relaxations of sparse polynomial optimization problems (2018)
  2. Fang, Xiaowei; Ni, Qin; Zeng, Meilan: A modified quasi-Newton method for nonlinear equations (2018)
  3. Huang, Shuai; Wan, Zhong; Zhang, Jing: An extended nonmonotone line search technique for large-scale unconstrained optimization (2018)
  4. Nikolovski, Filip; Stojkovska, Irena: Complex-step derivative approximation in noisy environment (2018)
  5. Autuori, Giuseppina; Cluni, Federico; Gusella, Vittorio; Pucci, Patrizia: Mathematical models for nonlocal elastic composite materials (2017)
  6. Bao, Ji-Feng; Li, Chong; Shen, Wei-Ping; Yao, Jen-Chih; Guu, Sy-Ming: Approximate Gauss-Newton methods for solving underdetermined nonlinear least squares problems (2017)
  7. Fan, Bin: A nonmonotone Levenberg-Marquardt method for nonlinear complementarity problems under local error bound (2017)
  8. Fang, Xiaowei; Ni, Qin: A frame-based conjugate gradients direct search method with radial basis function interpolation model (2017)
  9. Grapiglia, Geovani N.; Sachs, Ekkehard W.: On the worst-case evaluation complexity of non-monotone line search algorithms (2017)
  10. Huang, Linghua: A quasi-Newton algorithm for large-scale nonlinear equations (2017)
  11. Kimiaei, Morteza: A new class of nonmonotone adaptive trust-region methods for nonlinear equations with box constraints (2017)
  12. Kresoja, Milena; Lužanin, Zorana; Stojkovska, Irena: Adaptive stochastic approximation algorithm (2017)
  13. Li, Xiangrong; Wang, Bopeng; Hu, Wujie: A modified nonmonotone BFGS algorithm for unconstrained optimization (2017)
  14. Puranik, Yash; Sahinidis, Nikolaos V.: Bounds tightening based on optimality conditions for nonconvex box-constrained optimization (2017)
  15. Saeidian, Z.; Reza Peyghami, M.; Habibi, M.; Ghasemi, S.: A new trust-region method for solving systems of equalities and inequalities (2017)
  16. Salahi, Maziar: Exact two steps SOCP/SDP formulation for a modified conic trust region subproblem (2017)
  17. Verdério, Adriano; Karas, Elizabeth W.; Pedroso, Lucas G.; Scheinberg, Katya: On the construction of quadratic models for derivative-free trust-region algorithms (2017)
  18. Zhao, Xin; Fan, Jinyan: On the multi-point Levenberg-Marquardt method for singular nonlinear equations (2017)
  19. Amini, Keyvan; Rostami, Faramarz: Three-steps modified Levenberg-Marquardt method with a new line search for systems of nonlinear equations (2016)
  20. Bueno, L.F.; Haeser, G.; Martínez, J.M.: An inexact restoration approach to optimization problems with multiobjective constraints under weighted-sum scalarization (2016)

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