An Interior Subgradient Method for DC Programming with Proximal Distance Regularization
DOI:
https://doi.org/10.5540/03.2025.011.01.0340Palavras-chave:
DC Programming, Proximal Distance, Nonconvex Optimization, Subgradient MethodsResumo
This paper introduces an interior subgradient algorithm designed to tackle a specific category of nonconvex minimization problems, specifically focusing on minimizing DC functions (difference of two convex functions). The algorithm was inspired by the interior gradient method proposed by Auslender and Teboulle.
Downloads
Referências
A. Auslender and M. Teboulle. “Interior gradient and proximal methods for convex and conic optimization”. In: SIAM Journal on Optimization 16.3 (2006), pp. 697–725.
M. A. Bahraoui. “Diagonal Bundle Methods for Convex Minimization, Theoretical Aspect”. In: Int. J. Math. And Appl 6.4 (2018).
R. Burachik and J. Dutta. “Inexact proximal point methods for variational inequality problems”. In: SIAM Journal on Optimization 20.5 (2010), pp. 2653–2678.
F. H. Clarke. Optimization and nonsmooth analysis. SIAM, 1990.
J. X. Cruz Neto, J. O. Lopes, P. S. M. Santos, and J. C. O. Souza. “An interior proximal linearized method for DC programming based on Bregman distance or second-order homogeneous kernels”. In: Optimization 68.7 (2019), pp. 1305–1319.
J. X. Cruz Neto, P. R. Oliveira, A. Soubeyran, and J. C. O. Souza. “A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem”. In: Annals of Operations Research 289 (2020), pp. 313–339.
B. Lemaire. “On the convergence of some iterative methods for convex minimization”. In: Recent Developments in Optimization: Seventh French-German Conference on Optimization. Springer. 1995, pp. 252–268.
A. Moudafi and P.-E. Maingé. “On the convergence of an approximate proximal method for DC functions”. In: Journal of computational Mathematics (2006), pp. 475–480.
B. T. Polyak. “Introduction to optimization. Optimization software”. In: Inc., Publications Division, New York 1.32 (1987), p. 1.
R. Tyrrell Rockafellar and R. J.-B. Wets. Variational analysis. Vol. 317. Springer Science & Business Media, 2009.
J. C. O. Souza and P. R. Oliveira. “A proximal point algorithm for DC functions on Hadamard manifolds”. In: Journal of Global Optimization 63 (2015), pp. 797–810.
J. C. O. Souza, Paulo Roberto Oliveira, and Antoine Soubeyran. “Global convergence of a proximal linearized algorithm for difference of convex functions”. In: Optimization Letters 10.7 (2016), pp. 1529–1539.
W. Sun, Raimundo J. B. Sampaio, and M. A. B. Candido. “Proximal point algorithm for minimization of DC function”. In: Journal of computational Mathematics (2003), pp. 451–462.
