A Dynamic Alternating Direction of Multipliers for Nonconvex Minimization with Nonlinear Functional Equality Constraints

[1]  Jeffrey A. Fessler,et al.  Optimization Methods for Magnetic Resonance Image Reconstruction: Key Models and Optimization Algorithms , 2020, IEEE Signal Processing Magazine.

[2]  J. Royset Preface , 2019, Math. Program..

[3]  Marc Teboulle,et al.  Optimization on Spheres: Models and Proximal Algorithms with Computational Performance Comparisons , 2018, SIAM J. Math. Data Sci..

[4]  B. Mordukhovich Variational Analysis and Applications , 2018 .

[5]  Marc Teboulle,et al.  A simplified view of first order methods for optimization , 2018, Math. Program..

[6]  Marc Teboulle,et al.  Nonconvex Lagrangian-Based Optimization: Monitoring Schemes and Global Convergence , 2018, Math. Oper. Res..

[7]  Radu Ioan Bot,et al.  The Proximal Alternating Direction Method of Multipliers in the Nonconvex Setting: Convergence Analysis and Rates , 2018, Math. Oper. Res..

[8]  Marc Teboulle,et al.  First Order Methods beyond Convexity and Lipschitz Gradient Continuity with Applications to Quadratic Inverse Problems , 2017, SIAM J. Optim..

[9]  A. Montanari,et al.  The landscape of empirical risk for nonconvex losses , 2016, The Annals of Statistics.

[10]  Dimitri P. Bertsekas,et al.  Convex Optimization Algorithms , 2015 .

[11]  Marc Teboulle,et al.  Proximal alternating linearized minimization for nonconvex and nonsmooth problems , 2013, Mathematical Programming.

[12]  Guoyin Li,et al.  Global Convergence of Splitting Methods for Nonconvex Composite Optimization , 2014, SIAM J. Optim..

[13]  Marc Teboulle,et al.  Rate of Convergence Analysis of Decomposition Methods Based on the Proximal Method of Multipliers for Convex Minimization , 2014, SIAM J. Optim..

[14]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[15]  Heinrich von Stackelberg Market Structure and Equilibrium , 2010 .

[16]  Boris Polyak,et al.  B.S. Mordukhovich. Variational Analysis and Generalized Differentiation. I. Basic Theory, II. Applications , 2009 .

[17]  Adrian S. Lewis,et al.  The [barred L]ojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems , 2006, SIAM J. Optim..

[18]  Jianqing Fan,et al.  Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties , 2001 .

[19]  Dimitri P. Bertsekas,et al.  Constrained Optimization and Lagrange Multiplier Methods , 1982 .

[20]  R. Rockafellar Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming , 1974 .

[21]  M. Hestenes Multiplier and gradient methods , 1969 .

[22]  Radu Miculescu,et al.  Lipschitz Functions , 2019, Lecture Notes in Mathematics.

[23]  Marc Teboulle,et al.  Lagrangian methods for composite optimization , 2019, Handbook of Numerical Analysis.

[24]  Bastian Goldlücke,et al.  Variational Analysis , 2014, Computer Vision, A Reference Guide.

[25]  Marc Teboulle,et al.  Gradient-based algorithms with applications to signal-recovery problems , 2010, Convex Optimization in Signal Processing and Communications.

[26]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[27]  R. Glowinski,et al.  Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics , 1987 .

[28]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

[29]  B. Mercier,et al.  A dual algorithm for the solution of nonlinear variational problems via finite element approximation , 1976 .

[30]  M. Powell A method for nonlinear constraints in minimization problems , 1969 .

[31]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .