[1]
|
F. Alizadeh, J. Haeberly and M. Overton, Primal-dual interior-point methods for semidefinite programming: Convergence rates, stability and numerical results, SIAM Journal on Optimization, 8 (1998), 746-768.
doi: 10.1137/S1052623496304700.
|
[2]
|
M. ApS, The MOSEK optimization toolbox for MATLAB manual, version 8.0 (revision 60), 2017, http://docs.mosek.com/8.0/toolbox/index.html.
|
[3]
|
C. Bachoc, D. C. Gijswijt, A. Schrijver and F. Vallentin, Invariant Semidefinite Programs, Springer US, Boston, MA, 2012.
doi: 10.1007/978-1-4614-0769-0_9.
|
[4]
|
P. J. Coles, E. M. Metodiev and N. Ltkenhaus, Numerical approach for unstructured quantum key distribution, Nature Communications, 7 (2016), 11712.
|
[5]
|
B. Coutts, M. Girard and J. Watrous, Certifying optimality for convex quantum channel optimization problems, arXiv: 1810.13295, 2018.
|
[6]
|
D. den Hertog, Interior Point Approach to Linear, Quadratic and Convex Programming, Springer, Netherlands, 1994.
doi: 10.1007/978-94-011-1134-8.
|
[7]
|
D. den Hertog, C. Roos and T. Terlaky, On the classical logarithmic barrier function method for a class of smooth convex programming problems, J. Optim. Theory Appl., 73 (1992), 1-25.
doi: 10.1007/BF00940075.
|
[8]
|
D. Drusvyatskiy and H. Wolkowicz, The Many Faces of Degeneracy in Conic Optimization, now, 2017.
|
[9]
|
H. Fawzi, J. Saunderson and P. A. Parrilo, Semidefinite approximations of the matrix logarithm, Found. Comput. Math., 19 (2019), 259-296.
doi: 10.1007/s10208-018-9385-0.
|
[10]
|
H. Fawzi and O. Fawzi, Efficient optimization of the quantum relative entropy, J. Phys. A. Math. Theory, 51 (2018), 154003.
doi: 10.1088/1751-8121/aab285.
|
[11]
|
L. Faybusovich and C. Zhou, Long-step path-following algorithm for solving symmetric programming problems with nonlinear objective functions, Comput. Optim. Appl., 72 (2019), 769-795.
doi: 10.1007/s10589-018-0054-7.
|
[12]
|
L. Faybusovich and C. Zhou, Self-concordance and matrix monotonicity with applications to quantum entanglement problems, Applied Mathematics and Computation, 375 (2020), 125071.
doi: 10.1016/j.amc.2020.125071.
|
[13]
|
K. Fujisawa, M. Kojima and K. Nakata, Exploiting sparsity in primal-dual interior-point methods for semidefinite programming, Mathematical Programming, 79 (1997), 235-253.
doi: 10.1016/S0025-5610(97)00045-2.
|
[14]
|
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991.
doi: 10.1017/CBO9780511840371.
|
[15]
|
H.-K. Lo, M. Curty and K. Tamaki, Secure quantum key distribution, Nat. Photon., 8 (2014), 595-604.
|
[16]
|
Y. Nesterov, Lectures on Convex Optimization, Springer International Publishing, 2018.
doi: 10.1007/978-3-319-91578-4.
|
[17]
|
M. Pilanci and M. J. Wainwright, Newton sketch: A linear-time optimization algorithm with linear-quadratic convergence, 2015.
doi: 10.1137/15M1021106.
|
[18]
|
V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus and M. Peev, The security of practical quantum key distribution, Rev. Mod. Phys., 81 (2009), 1301-1350.
|
[19]
|
K. C. Toh, M. J. Todd and R. H. Tütüncü, SDPT3 –- a MATLAB software package for semidefinite programming, optimization methods and software, Optimization Methods and Software, 11 (1999), 545-581.
doi: 10.1080/10556789908805762.
|
[20]
|
L. Vandenberghe and M. S. Andersen, Chordal Graphs and Semidefinite Optimization, Now Publishers, 2015.
|
[21]
|
A. Winick, N. Lütkenhaus and P. J. Coles, Reliable numerical key rates for quantum key distribution, Quantum, 2 (2018), 77.
|