Convergence of Augmented Lagrangian Methods for Composite Optimization Problems

References

• [1] Andreani R, Birgin EG, Martínez JM, Schuverdt ML (2008) On augmented Lagrangian methods with general lower-level constraints. SIAM J. Optim. 18(4):1286–1309.Crossref, Google Scholar
• [2] Aragón Artacho FJ, Geoffroy MH (2008) Characterization of metric regularity of subdifferentials. J. Convex Anal. 15(2):365–380.Google Scholar
• [3] Bauschke HH, Borwein JM, Li W (1999) Strong conical hull intersection property, bounded linear regularity, Jameson’s property (G), and error bounds in convex optimization. Math. Programming 86:135–160.Crossref, Google Scholar
• [4] Birgin EG, Haeser G, Ramos A (2018) Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points. Comput. Optim. Appl. 69:51–75.Crossref, Google Scholar
• [5] Bonnans JF, Shapiro A (2000) Perturbation Analysis of Optimization Problems (Springer, New York).Crossref, Google Scholar
• [6] Chieu NH, Hien LV, Nghia TTA, Tuan HA (2021) Quadratic growth and strong metric subregularity of the subdifferential via subgradient graphical derivative. SIAM J. Optim. 31(1):545–568.Crossref, Google Scholar
• [7] De Marchi A, Mehlitz P (2024) Local properties and augmented Lagrangians in fully nonconvex composite optimization. J. Nonsmooth Anal. Optim. 5:12235.Crossref, Google Scholar
• [8] Dontchev AL, Rockafellar RT (2014) Implicit Functions and Solution Mappings: A View from Variational Analysis, 2nd ed. (Springer, New York).Crossref, Google Scholar
• [9] Fernández D, Solodov MV (2012) Local convergence of exact and inexact augmented Lagrangian methods under the second-order sufficient optimality condition. SIAM J. Optim. 22(2):384–407.Crossref, Google Scholar
• [10] Fischer A (2002) Local behavior of an iterative framework for generalized equations with nonisolated solutions. Math. Programming 94:91–124.Crossref, Google Scholar
• [11] Hang NTV, Sarabi ME (2021) Local convergence analysis of augmented Lagrangian methods for piecewise linear-quadratic composite optimization problems. SIAM J. Optim. 31(4):2665–2694.Crossref, Google Scholar
• [12] Hang NTV, Mordukhovich BS, Sarabi ME (2020) Second-order variational analysis in second-order cone programming. Math. Programming 180:75–106.Crossref, Google Scholar
• [13] Hestenes MR (1969) Multiplier and gradient methods. J. Optim. Theory Appl. 4:303–320.Crossref, Google Scholar
• [14] Ioffe AD (2017) Variational Analysis of Regular Mappings: Theory and Applications (Springer, Cham, Switzerland).Crossref, Google Scholar
• [15] Izmailov AF, Kurennoy AS (2013) Abstract Newtonian frameworks and their applications. SIAM J. Optim. 23(4):2369–2396.Crossref, Google Scholar
• [16] Izmailov AF, Solodov MV (2014) Newton-Type Methods for Optimization and Variational Problems (Springer, Cham, Switzerland).Crossref, Google Scholar
• [17] Kan C, Song W (2015) Augmented Lagrangian duality for composite optimization problems. J. Optim. Theory Appl. 165:763–784.Crossref, Google Scholar
• [18] Kanzow C, Steck D (2019) Improved local convergence results for augmented Lagrangian methods in C2-cone reducible constrained optimization. Math. Program. 177:425–438.Crossref, Google Scholar
• [19] Milzarek A (2016) Numerical methods and second order theory for nonsmooth problems. PhD dissertation, University of Munich, Munich.Google Scholar
• [20] Mohammadi A, Sarabi ME (2020) Twice epi-differentiability of extended-real-valued functions with applications in composite optimization. SIAM J. Optim. 30(3):2379–2409.Crossref, Google Scholar
• [21] Mohammadi A, Mordukhovich BS, Sarabi ME (2021) Parabolic regularity via geometric variational analysis. Trans. Amer. Math. Soc. 374(3):1711–1763.Crossref, Google Scholar
• [22] Mordukhovich BS, Sarabi ME (2019) Criticality of Lagrange multipliers in variational systems. SIAM J. Optim. 29(2):1524–1557.Crossref, Google Scholar
• [23] Poliquin RA, Rockafellar RT (1996) Prox-regular functions in variational analysis. Trans. Amer. Math. Soc. 348(5):1805–1838.Crossref, Google Scholar
• [24] Powell MJD (1969) A method for nonlinear constraints in minimization problems. Fletcher R, ed. Optimization (Academic Press, New York), 283–298.Google Scholar
• [25] Robinson SM (1981) Some continuity properties of polyhedral multifunctions. Math. Program. Stud. 14:206–214.Crossref, Google Scholar
• [26] Rockafellar RT (1973) A dual approach to solving nonlinear programming problems by unconstrained optimization. Math. Programming 5:354–373.Crossref, Google Scholar
• [27] Rockafellar RT (2023) Augmented Lagrangians and hidden convexity in sufficient conditions for local optimality. Math. Program. 198:159–194.Crossref, Google Scholar
• [28] Rockafellar RT (2023) Convergence of augmented Lagrangian methods in extensions beyond nonlinear programming. Math. Program. 199:375–420.Crossref, Google Scholar
• [29] Rockafellar RT, Wets RJB (1998) Variational Analysis (Springer-Verlag, Berlin, Heidelberg).Crossref, Google Scholar
• [30] Sarabi ME (2022) Primal superlinear convergence of SQP methods for piecewise linear-quadratic composite optimization problems. Set-Valued Var. Anal. 30:1–37.Crossref, Google Scholar
• [31] Shapiro A (2003) On a class of nonsmooth composite functions. Math. Oper. Res. 28(4):677–692.Link, Google Scholar
• [32] Shapiro A, Sun J (2004) Some properties of the augmented Lagrangian in cone constrained optimization. Math. Oper. Res. 29(3):479–491.Link, Google Scholar
• [33] Sun D, Sun J, Zhang L (2008) The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming. Math. Programming 114:349–391.Crossref, Google Scholar
• [34] Wang S, Ding C (2024) Local convergence analysis of augmented Lagrangian method for nonlinear semidefinite programming. Comput. Optim. Appl. 87:39–87.Crossref, Google Scholar
• [35] Wang S, Ding C, Zhang Y, Zhao X (2023) Strong variational sufficiency for nonlinear semidefinite programming and its implications. SIAM J. Optim. 33(4):2998–3011.Crossref, Google Scholar