The Exact Modulus of the Generalized Concave Kurdyka-Łojasiewicz Property
References
- [1] (2010) Proximal alternating minimization and projection methods for nonconvex problems: An approach based on the Kurdyka-Łojasiewicz inequality. Math. Oper. Res. 35(2):438–457.Link, Google Scholar
- [2] (2019) A general double-proximal gradient algorithm for d.c. programming. Math. Program. 178(1):301–326.Crossref, Google Scholar
- [3] (2017) Convex Analysis and Monotone Operator Theory in Hilbert Spaces (Springer, Cham).Crossref, Google Scholar
- [4] (2007) The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems. SIAM J. Optim. 17(4):1205–1223.Crossref, Google Scholar
- [5] (2014) Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Programming 146(1):459–494.Crossref, Google Scholar
- [6] (2007) Clarke subgradients of stratifiable functions. SIAM J. Optim. 18(2):556–572.Crossref, Google Scholar
- [7] (2010) Characterizations of Łojasiewicz inequalities: Subgradient flows, talweg, convexity. Trans. Amer. Math. Soc. 362(6):3319–3363.Crossref, Google Scholar
- [8] (2017) From error bounds to the complexity of first-order descent methods for convex functions. Math. Programming 165(2):471–507.Crossref, Google Scholar
- [9] (1998) On gradients of functions definable in o-minimal structures. Ann. Inst. Fourier (Grenoble) 48(3):769–783.Crossref, Google Scholar
- [10] (2018) Calculus of the exponent of Kurdyka-Łojasiewicz inequality and its applications to linear convergence of first-order methods. Foundations Comput. Math. 18(5):1199–1232.Crossref, Google Scholar
- [11] (2019) A refined convergence analysis of pDCAe with applications to simultaneous sparse recovery and outlier detection. Comput. Optim. Appl. 73:69–100.Crossref, Google Scholar
- [12] (1963) Une propriété topologique des sous-ensembles analytiques réels. Les équations aux Dérivées Partielles 117:87–89.Google Scholar
- [13] (2006) Variational Analysis and Generalized Differentiation I: Basic Theory (Springer-Verlag, Berlin).Crossref, Google Scholar
- [14] (2014) iPiano: Inertial proximal algorithm for nonconvex optimization. SIAM J. Imaging Sci. 7(2):1388–1419.Crossref, Google Scholar
- [15] (2015) Real Mathematical Analysis (Springer, Cham).Crossref, Google Scholar
- [16] (1970) Convex Analysis (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
- [17] (1998) Variational Analysis (Springer-Verlag, Berlin).Crossref, Google Scholar
- [18] (2015) An Introduction to Classical Real Analysis (American Mathematical Society, Providence, RI).Crossref, Google Scholar
- [19] (2018) A proximal difference-of-convex algorithm with extrapolation. Comput. Optim. Appl. 69:297–324.Crossref, Google Scholar
- [20] (2019) Projection onto Minkowski sums with application to constrained learning. Proc. 36th Internat. Conf. Machine Learning, vol. 97 (PMLR, Cambridge, MA), 3642–3651.Google Scholar
- [21] (2019) Deducing Kurdyka-Łojasiewicz exponent via inf-projection. Preprint, submitted February 10, https://arxiv.org/abs/1902.03635.Google Scholar
- [22] (2021) Convergence rate analysis of a sequential convex programming method with line search for a class of constrained difference-of-convex optimization problems. SIAM J. Optim. 31(3):2024–2054.Crossref, Google Scholar

