An Adaptive Lagrangian-Based Scheme for Nonconvex Composite Optimization
Published Online:4 Jan 2023https://doi.org/10.1287/moor.2022.1342
References
- [1] (1982) Constrained Optimization and Lagrangian Multipliers (Academic Press, New York).Google Scholar
- [2] (1999) Nonlinear Programming (Athena Scientific, Belmont, MA).Google Scholar
- [3] (1989) Parallel and Distributed Computation: Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ).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] (2013) Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Programming 146(1–2):459–494.Crossref, Google Scholar
- [6] (2018) Nonconvex Lagrangian-based optimization: Monitoring schemes and global convergence. Math. Oper. Res. 43(4):1210–1232.Link, Google Scholar
- [7] (2007) Clarke subgradients of stratifiable functions. SIAM J. Optim. 18(2):556–572.Crossref, Google Scholar
- [8] (2020) The proximal alternating direction method of multipliers in the nonconvex setting: Convergence analysis and rates. Math. Oper. Res. 45(2):682–712.Link, Google Scholar
- [9] (1992) Optimality conditions for non-finite valued convex composite functions. Math. Programming 57:103–120.Crossref, Google Scholar
- [10] (2018) Error bounds, quadratic growth, and linear convergence of proximal methods. Math. Oper. Res. 43(3):919–948.Link, Google Scholar
- [11] (1983) Augmented Lagrangian Methods: Applications to the Solution of Boundary-Valued Problems, vol.15 (Elsevier, Amsterdam), 1–340.Google Scholar
- [12] (1983) Applications of the method of multipliers to variational inequalities. Fortin M, Glowinski R, eds. Augmented Lagrangian Methods: Applications to the Solution of Boundary-Valued Problems (North Holland, Amsterdam), 299–331.Crossref, Google Scholar
- [13] (1989) Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics (Society for Industrial and Applied Mathematics, Philadelphia).Crossref, Google Scholar
- [14] (2016) A proximal method for composite minimization. Math. Programming Ser. A 158:501–546.Crossref, Google Scholar
- [15] (2015) Global convergence of splitting methods for nonconvex composite optimization. SIAM J. Optim. 25(4):2434–2460.Crossref, Google Scholar
- [16] (2018) The landscape of empirical risk for nonconvex losses. Ann. Statist. 46(6A):2747–2774.Crossref, Google Scholar
- [17] (1998) Variational Analysis (Springer, Berlin Heidelberg).Crossref, Google Scholar
- [18] (2019) Lagrangian methods for composite optimization. Kimmel R, Tai XC, eds. Processing, Analyzing and Learning of Images, Shapes, and Forms (North Holland), 401–436.Crossref, Google Scholar

