Convergent Nested Alternating Minimization Algorithms for Nonconvex Optimization Problems
References
- [1] (1991) The constrained total least squares technique and its applications to harmonic superresolution. IEEE Trans. Signal Processing 39(5):1070–1087.Crossref, Google Scholar
- [2] (2009) On the convergence of the proximal algorithm for nonsmooth functions involving analytic features. Math. Programming 116(1-2):5–16.Crossref, Google Scholar
- [3] (2013) Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods. Math. Programming 137(1-2):91–129.Crossref, Google Scholar
- [4] (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
- [5] (2017) First-Order Methods in Optimization (SIAM, Philadelphia).Crossref, Google Scholar
- [6] (2006) On the solution of the Tikhonov regularization of the total least squares problem. SIAM J. Optim. 17(1):98–118.Crossref, Google Scholar
- [7] (2009) Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. Image Processing 18(11):2419–2434.Crossref, Google Scholar
- [8] (2016) An alternating semiproximal method for nonconvex regularized structured total least squares problems. SIAM J. Matrix Anal. Appl. 37(3):1129–1150.Crossref, Google Scholar
- [9] (2007) The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems. SIAM J. Optim. 17(4):1205–1223.Crossref, Google Scholar
- [10] (2014) Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Programming 146(1-2):459–494.Crossref, Google Scholar
- [11] (2018) First order methods beyond convexity and lipschitz gradient continuity with applications to quadratic inverse problems. SIAM J. Optim. 28(3):2131–2151.Crossref, Google Scholar
- [12] (2018) A block coordinate variable metric linesearch based proximal gradient method. Comput. Optim. Appl. 71(1):5–52.Crossref, Google Scholar
- [13] (2016) A block coordinate variable metric forward–backward algorithm. J. Global Optim. 66(3):457–485.Crossref, Google Scholar
- [14] (2015) Splitting methods with variable metric for Kurdyka–łojasiewicz functions and general convergence rates. J. Optim. Theory Appl. 165(3):874–900.Crossref, Google Scholar
- [15] (1980) An analysis of the total least squares problem. SIAM J. Numer. Anal. 17(6):883–893.Crossref, Google Scholar
- [16] (1999) Tikhonov regularization and total least squares. SIAM J. Matrix Anal. Appl. 21(1):185–194.Crossref, Google Scholar
- [17] (2016) Multidimensional scaling by majorization: A review. J. Statist. Software 73(8):1–26.Crossref, Google Scholar
- [18] (2016) Stochastic multi-objective optimization: A survey on non-scalarizing methods. Ann. Oper. Res. 236(2):475–499.Crossref, Google Scholar
- [19] (2006) Deblurring Images: Matrices, Spectra, and Filtering (SIAM, Philadelphia).Crossref, Google Scholar
- [20] (2015) Proximal heterogeneous block implicit-explicit method and application to blind ptychographic diffraction imaging. SIAM J. Imaging Sci. 8(1):426–457.Crossref, Google Scholar
- [21] (2017) Non-convex optimization for machine learning. Foundations Trends Machine Learning 10(3–4):142–336.Crossref, Google Scholar
- [22] (1998) On gradients of functions definable in o-minimal structures. Ann. Inst. Fourier 48(3):769–783.Crossref, Google Scholar
- [23] (1963) Une propriété topologique des sous-ensembles analytiques réels. Les Équations aux Dérivées Partielles (Paris, 1962) (Éditions du Centre National de la Recherche Scientifique, Paris), 87–89.Google Scholar
- [24] (2020) Evolutionary computation, optimization, and learning algorithms for data science. Amini MH, ed. Optimization, Learning, and Control for Interdependent Complex Networks (Springer, Cham, Switzerland), 37–65.Crossref, Google Scholar
- [25] (2006) Variational Analysis and Generalized Differentiation I: Basic Theory (Springer, Berlin).Crossref, Google Scholar
- [26] (1965) Proximité et dualité dans un espace hilbertien. Bull. Soc. Math. France 93:273–299.Crossref, Google Scholar
- [27] (1983) A method for solving the convex programming problem with convergence rate O(1/k2). Dokl. Akad. Nauk SSSR 269(3):543–547.Google Scholar
- [28] (2019) Unifying abstract inexact convergence theorems and block coordinate variable metric iPiano. SIAM J. Optim. 29(1):541–570.Crossref, Google Scholar
- [29] (2014) iPiano: Inertial proximal algorithm for nonconvex optimization. SIAM J. Imaging Sci. 7(2):1388–1419.Crossref, Google Scholar
- [30] (2018) Cooperative localization in WSNs: A hybrid convex/nonconvex solution. IEEE Trans. Signal Inform. Processing Networks 4(1):162–172.Crossref, Google Scholar
- [31] (2016) Inertial proximal alternating linearized minimization (iPALM) for nonconvex and nonsmooth problems. SIAM J. Imaging Sci. 9(4):1756–1787.Crossref, Google Scholar
- [32] (2009) Variational Analysis (Springer, Berlin).Google Scholar
- [33] (2018) A smoothing alternating minimization-based algorithm for clustering with sum-min of Euclidean norms. Pure Appl. Funct. Anal. 3:653–679.Google Scholar
- [34] (2018) A survey on nonconvex regularization-based sparse and low-rank recovery in signal processing, statistics, and machine learning. IEEE Access 6:69883–69906.Crossref, Google Scholar
- [35] (2017) A globally convergent algorithm for nonconvex optimization based on block coordinate update. J. Sci. Comput. 72(2):700–734.Crossref, Google Scholar

