Complex Optimization Toolbox

The Complex Optimization Toolbox is a MATLAB toolbox for optimizing problems in complex variables, although real optimization is also possible and is without performance penalty. Included are generalized algorithms for unconstrained nonlinear optimization: nonlinear conjugate gradient and limited-memory BFGS with Moré–Thuente line search or dogleg trust region, nonlinear least squares: minimization of vector-, matrix- or tensor-valued residual functions, complex bound constraints, Levenberg–Marquardt and Gauss–Newton with CG–Steihaug or dogleg trust region, and much more: automated numerical real and complex differentiation, preservation of unknowns in their original format (i.e., as a vector, matrix, tensor or even a cell array of tensors), preconditioned conjugate gradient, … The Complex Optimization Toolbox is part of Tensorlab, a MATLAB toolbox for tensor computations. Please consult the Tensorlab user guide to get started with the Complex Optimization Toolbox. Alternatively, see the toolbox’s Contents.m for an overview of its functionality. For questions, bug reports or other inquiries, please contact

References in zbMATH (referenced in 10 articles )

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  1. Josz, Cédric; Molzahn, Daniel K.: Lasserre hierarchy for large scale polynomial optimization in real and complex variables (2018)
  2. Che, Maolin; Qi, Liqun; Wei, Yimin: Iterative algorithms for computing US- and U-eigenpairs of complex tensors (2017)
  3. Jiang, Bo; Li, Zhening; Zhang, Shuzhong: Characterizing real-valued multivariate complex polynomials and their symmetric tensor representations (2016)
  4. Sorber, Laurent; Domanov, Ignat; Van Barel, Marc; De Lathauwer, Lieven: Exact line and plane search for tensor optimization (2016)
  5. Van Barel, Marc: Designing rational filter functions for solving eigenvalue problems by contour integration (2016)
  6. Zhang, Songchuan; Xia, Youshen; Zheng, Weixing: A complex-valued neural dynamical optimization approach and its stability analysis (2015)
  7. Audibert, Lorenzo; Haddar, Houssem: A generalized formulation of the linear sampling method with exact characterization of targets in terms of farfield measurements (2014)
  8. Ricaud, Benjamin; Stempfel, Guillaume; Torrésani, Bruno; Wiesmeyr, Christoph; Lachambre, Hélène; Onchis, Darian: An optimally concentrated Gabor transform for localized time-frequency components (2014)
  9. Le, Thanh Hieu; Sorber, Laurent; Van Barel, Marc: The Pythagoras number of real sum of squares polynomials and sum of square magnitudes of polynomials (2013)
  10. Sorber, Laurent; Van Barel, Marc; De Lathauwer, Lieven: Unconstrained optimization of real functions in complex variables (2012)