References
- Birgin EG, Martínez JM, Raydan M. Nonmonotone spectral projected gradient methods on convex sets. SIAM J Optim. 2000;10:1196–1211.
- Grippo L, Lampariello F, Lucidi S. A nonmonotone line search technique for Newton's method. SIAM J Numer Anal. 1986;23(4):707–716.
- Barzilai J, Borwein JM. Two-point step size gradient methods. IMA J Numer Anal. 1988;8(1):141–148.
- Andretta M, Birgin EG, Martínez JM. Partial spectral projected gradient method with active-set strategy for linearly constrained optimization. Numer Algorithms. 2009;53:23–52.
- Birgin EG, Martínez JM, Raydan M. Algorithm 813: SPG – software for convex-constrained optimization. ACM Trans Math Softw. 2001;27:3340–349.
- Birgin EG, Martínez JM, Raydan M. Spectral projected gradient methods: review and perspectives. J Stat Softw. 2014;60(3):1–21.
- Cores D, Escalante R, González-Lima M, et al. On the use of the spectral projected gradient method for support vector machines. J Comput Appl Math. 2009;28:327–364.
- Gomes-Ruggiero MA, Martínez JM, Santos SA. Spectral projected gradient method with inexact restoration for minimization with nonconvex constraints. J Sci Comput. 2009;31(3):1628–1652.
- Guerrero J, Raydan M, Rojas M. A hybrid-optimization method for large-scale non-negative full regularization in image restoration. Inver Probl Sci En. 2011;21:741–766.
- Liu J, Duan Y. Two spectral gradient projection methods for constrained equations and their linear convergence rate. J Inequal Appl. 2015;2015(1):8.
- Martínez JM, Pilotta EA, Raydan M. Spectral gradient methods for linearly constrained optimization. J Optim Theor Appl. 2005;125:629–651.
- Wang C, Liu Q, Yang X. Convergence properties of nonmonotone spectral projected gradient methods. J Comput Appl Math. 2005;182:51–66.
- Yu Z, Lin J, Sun J, et al. Spectral gradient projection method for monotone nonlinear equations with convex constraints. Appl Numer Math. 2009;59(10):2416–2423.
- Zhang L, Zhou W. Spectral gradient projection method for solving nonlinear monotone equations. J Comput Appl Math. 2006;196(2):478–484.
- Birgin EG, Martínez JM, Raydan M. Inexact spectral projected gradient methods on convex sets. IMA J Numer Anal. 2003;23:539–559.
- Andreani R, Birgin EG, Martínez JM, et al. Spectral projected gradient and variable metric methods for optimization with linear inequalities. IMA J Numer Anal. 2005;25:221–252.
- Boyle JP, Dykstra RL. A method for finding projections onto the intersection of convex sets in Hilbert spaces. In: Dykstra R, Robertson T, and Wright FT, editors. Advances in order restricted statistical inference. New York, NY: Springer; 1986. p. 28–47.
- Dunn JC. Convergence rates for conditional gradient sequences generated by implicit step length rules. SIAM J Control Optim. 1980;18(5):473–487.
- Frank M, Wolfe P. An algorithm for quadratic programming. Nav Res Logist Q. 1956;3:1–295–110.
- Freund R, Grigas P. New analysis and results for the Frank-Wolfe method. Math Program. 2014. p. 1–32.
- Jaggi M. Revisiting Frank-Wolfe: Projection-free sparse convex optimization. Proceedings of the 30th International Conference on Machine Learning (ICML-13); Vol. 28, 2013. p. 427–435.
- Gould NIM, Orban D, Toint PL. Cuter, a constrained and unconstrained testing environment, revisited. ACM Trans Math Softw. 2003;29:373–394.
- Huyer W, Neumaier A. MINQ8: general definite and bound constrained indefinite quadratic programming. Comput Optim Appl. 2018;69:351–381.
- Guélat J, Marcotte P. Some comments on Wolfe's ‘away step’. Math Program. 1986;35:110–119.
- Nocedal J, Wright SJ. Numerical optimization. 2nd ed. New York, NY, USA: Springer; 2006.
- Powell MJD. Log barrier methods for semi-infinite programming calculations. In: Lipitakis EA, editor. Advances on computer mathematics and its applications. 1993. p. 1–21.
- Woodgate KG. Least-squares solution of F = PG over positive semidefinite symmetric P. Linear Algebra Appl. 1996;245:171–190.
- Gonçalves D, Gomes-Ruggiero M, Lavor C. A projected gradient method for optimization over density matrices. Optim Meth Softw. 2016;31(2):328–341.
- Higham NJ. Computing a nearest symmetric positive semidefinite matrix. Linear Algebra Appl. 1988;103:103–118.
- Gonçalves DS, Gonçalves MLN, Oliveira FR. Levenberg-Marquardt methods with inexact projections for constrained nonlinear systems. Aug 2019. arXiv:1908.06118.
- Toh K-C. An inexact primal–dual path following algorithm for convex quadratic SDP. Math Program. 2008;112(1):221–254.
- Garber D. Faster projection-free convex optimization over the spectrahedron. Adv Neural Inf Processing Syst. 2016. p. 874–882.
- Allen-Zhu Z, Hazan E, Hu W, et al. Linear convergence of a Frank-Wolfe type algorithm over trace-norm balls. Adv. Neural Inf. Processing Syst. 2017. p. 6191–6200.
- Ding L, Fei Y, Xu Q, et al. Spectral Frank-Wolfe algorithm: Strict complementarity and linear convergence. Proceedings of the 37th International Conference on Machine Learning; 2020.