A Primal-Dual Splitting Algorithm for Finding Zeros of Sums of Maximal Monotone Operators

We consider the primal problem of finding the zeros of the sum of a maximal monotone operator and the composition of another maximal monotone operator with a linear continuous operator. By formulat...

[1]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[2]  Radu Ioan Bot,et al.  Convergence Analysis for a Primal-Dual Monotone + Skew Splitting Algorithm with Applications to Total Variation Minimization , 2012, Journal of Mathematical Imaging and Vision.

[3]  Heinz H. Bauschke,et al.  Attouch-Théra duality revisited: Paramonotonicity and operator splitting , 2011, J. Approx. Theory.

[4]  Bang Công Vu,et al.  A splitting algorithm for dual monotone inclusions involving cocoercive operators , 2011, Advances in Computational Mathematics.

[5]  P. L. Combettes,et al.  Primal-Dual Splitting Algorithm for Solving Inclusions with Mixtures of Composite, Lipschitzian, and Parallel-Sum Type Monotone Operators , 2011, Set-Valued and Variational Analysis.

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

[7]  Antonin Chambolle,et al.  A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging , 2011, Journal of Mathematical Imaging and Vision.

[8]  Heinz H. Bauschke,et al.  Convex Analysis and Monotone Operator Theory in Hilbert Spaces , 2011, CMS Books in Mathematics.

[9]  Tony F. Chan,et al.  A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science , 2010, SIAM J. Imaging Sci..

[10]  Patrick L. Combettes,et al.  A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality , 2010, SIAM J. Optim..

[11]  R. Boţ,et al.  Conjugate Duality in Convex Optimization , 2010 .

[12]  Shiqian Ma,et al.  Fast Multiple-Splitting Algorithms for Convex Optimization , 2009, SIAM J. Optim..

[13]  R. Boţ,et al.  Regularity conditions via generalized interiority notions in convex optimization: New achievements and their relation to some classical statements , 2009, 0906.0453.

[14]  Gonzalo Alduncin,et al.  Composition duality principles for mixed variational inequalities , 2005, Math. Comput. Model..

[15]  Michael C. Ferris,et al.  Smooth methods of multipliers for complementarity problems , 1999, Math. Program..

[16]  Teemu Pennanen,et al.  Dualization of Generalized Equations of Maximal Monotone Type , 1999, SIAM J. Optim..

[17]  Z. Drezner.  A note on accelerating the weiszfeld procedure , 1995 .

[18]  Dimitri P. Bertsekas,et al.  On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators , 1992, Math. Program..

[19]  M. Shirosaki.  Another proof of the defect relation for moving targets , 1991 .

[20]  J. Spingarn.  Partial inverse of a monotone operator , 1983 .

[21]  B. V. Dean,et al.  Studies in Linear and Non-Linear Programming. , 1959 .

[22]  Jonathan Eckstein.  Augmented Lagrangian and Alternating Direction Methods for Convex Optimization: A Tutorial and Some Illustrative Computational Results , 2012 .

[23]  S. Simons.  From Hahn-Banach to monotonicity , 2008 .

[24]  M. Nikolova.  An Algorithm for Total Variation Minimization and Applications , 2004 .

[25]  C. Zălinescu.  Convex analysis in general vector spaces , 2002 .

[26]  Paul Tseng,et al.  A Modified Forward-backward Splitting Method for Maximal Monotone Mappings 1 , 1998 .

[27]  H. Attouch.  A General Duality Principle for the Sum of Two Operators 1 , 1996 .

[28]  George O. Wesolowsky,et al.  FACILITIES LOCATION: MODELS AND METHODS , 1988 .

[29]  I. Ekeland,et al.  Convex analysis and variational problems , 1976 .