An Adaptive Lagrangian-Based Scheme for Nonconvex Composite Optimization

Published Online:https://doi.org/10.1287/moor.2022.1342

References

  • [1] Bertsekas D (1982) Constrained Optimization and Lagrangian Multipliers (Academic Press, New York).Google Scholar
  • [2] Bertsekas D (1999) Nonlinear Programming (Athena Scientific, Belmont, MA).Google Scholar
  • [3] Bertsekas D, Tsitsiklis JN (1989) Parallel and Distributed Computation: Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ).Google Scholar
  • [4] Bolte J, Daniilidis A, Lewis A (2007) The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems. SIAM J. Optim. 17(4):1205–1223.CrossrefGoogle Scholar
  • [5] Bolte J, Sabach S, Teboulle M (2013) Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Programming 146(1–2):459–494.CrossrefGoogle Scholar
  • [6] Bolte J, Sabach S, Teboulle M (2018) Nonconvex Lagrangian-based optimization: Monitoring schemes and global convergence. Math. Oper. Res. 43(4):1210–1232.LinkGoogle Scholar
  • [7] Bolte J, Daniilidis A, Lewis A, Shiota M (2007) Clarke subgradients of stratifiable functions. SIAM J. Optim. 18(2):556–572.CrossrefGoogle Scholar
  • [8] Boţ RI, Nguyen DK (2020) The proximal alternating direction method of multipliers in the nonconvex setting: Convergence analysis and rates. Math. Oper. Res. 45(2):682–712.LinkGoogle Scholar
  • [9] Burke JV, Poliquin RA (1992) Optimality conditions for non-finite valued convex composite functions. Math. Programming 57:103–120.CrossrefGoogle Scholar
  • [10] Drusvyatskiy D, Lewis AS (2018) Error bounds, quadratic growth, and linear convergence of proximal methods. Math. Oper. Res. 43(3):919–948.LinkGoogle Scholar
  • [11] Fortin M, Glowinski R (1983) Augmented Lagrangian Methods: Applications to the Solution of Boundary-Valued Problems, vol.15 (Elsevier, Amsterdam), 1–340.Google Scholar
  • [12] Gabay D (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.CrossrefGoogle Scholar
  • [13] Glowinski R, Le Tallec P (1989) Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics (Society for Industrial and Applied Mathematics, Philadelphia).CrossrefGoogle Scholar
  • [14] Lewis AS, Wright SJ (2016) A proximal method for composite minimization. Math. Programming Ser. A 158:501–546.CrossrefGoogle Scholar
  • [15] Li G, Pong TK (2015) Global convergence of splitting methods for nonconvex composite optimization. SIAM J. Optim. 25(4):2434–2460.CrossrefGoogle Scholar
  • [16] Mei S, Bai Y, Montanari A (2018) The landscape of empirical risk for nonconvex losses. Ann. Statist. 46(6A):2747–2774.CrossrefGoogle Scholar
  • [17] Rockafellar RT, Wets RJB (1998) Variational Analysis (Springer, Berlin Heidelberg).CrossrefGoogle Scholar
  • [18] Sabach S, Teboulle M (2019) Lagrangian methods for composite optimization. Kimmel R, Tai XC, eds. Processing, Analyzing and Learning of Images, Shapes, and Forms (North Holland), 401–436.CrossrefGoogle Scholar
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