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 30 articles )

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  1. Khouja, Rima; Khalil, Houssam; Mourrain, Bernard: Riemannian Newton optimization methods for the symmetric tensor approximation problem (2022)
  2. Aghamiry, Hossein S.; Gholami, Ali; Operto, Stéphane: Complex-valued imaging with total variation regularization: an application to full-waveform inversion in visco-acoustic media (2021)
  3. Brust, Johannes J.; Di, Zichao (Wendy); Leyffer, Sven; Petra, Cosmin G.: Compact representations of structured BFGS matrices (2021)
  4. Fu, Taoran; Jiang, Bo; Li, Zhening: On decompositions and approximations of conjugate partial-symmetric tensors (2021)
  5. Kollnig, Konrad; Bientinesi, Paolo; Di Napoli, Edoardo A.: Rational spectral filters with optimal convergence rate (2021)
  6. Fung, Samy Wu; Di, Zichao: Multigrid optimization for large-scale ptychographic phase retrieval (2020)
  7. Liu, Shuxin; Jiang, Haijun; Zhang, Liwei; Mei, Xuehui: A neurodynamic optimization approach for complex-variables programming problem (2020)
  8. Li, Yuan: Exterior Steklov eigenvalues and modified exterior Steklov eigenvalues in inverse scattering (2020)
  9. Mowakeaa, Rami; Boukouvalas, Zois; Long, Qunfang; Adali, Tülay: IVA using complex multivariate GGD: application to fMRI analysis (2020)
  10. Kürschner, Patrick: Approximate residual-minimizing shift parameters for the low-rank ADI iteration (2019)
  11. Li, Lu; Wang, Lun; Wang, Guoqiang; Li, Na; Zhang, Juli: Linearized alternating direction method of multipliers for separable convex optimization of real functions in complex domain (2019)
  12. Rahpeymaii, Farzad; Amini, Keyvan; Allahviranloo, Tofigh; Malkhalifeh, Mohsen Rostamy: A new class of conjugate gradient methods for unconstrained smooth optimization and absolute value equations (2019)
  13. Vervliet, Nico; Debals, Otto; De Lathauwer, Lieven: Exploiting efficient representations in large-scale tensor decompositions (2019)
  14. Cogar, Samuel: A modified transmission eigenvalue problem for scattering by a partially coated crack (2018)
  15. Cogar, S.; Colton, D.; Monk, P.: Using eigenvalues to detect anomalies in the exterior of a cavity (2018)
  16. Josz, Cédric; Molzahn, Daniel K.: Lasserre hierarchy for large scale polynomial optimization in real and complex variables (2018)
  17. Kuo, Yueh-Cheng; Lee, Tsung-Lin: Computing the unique CANDECOMP/PARAFAC decomposition of unbalanced tensors by homotopy method (2018)
  18. Li, L.; Wang, G. Q.; Zhang, J. L.: On the (O(1/K)) convergence rate of the alternating direction method of multipliers in a complex domain (2018)
  19. Liu, Jialin; Garcia-Cardona, Cristina; Wohlberg, Brendt; Yin, Wotao: First- and second-order methods for online convolutional dictionary learning (2018)
  20. Audibert, Lorenzo; Haddar, Houssem: The generalized linear sampling method for limited aperture measurements (2017)

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