Duality and Dual Methods

[1]  Bingsheng He,et al.  The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent , 2014, Mathematical Programming.

[2]  Leonid Hurwicz Programming in Linear Spaces , 2014 .

[3]  Renato D. C. Monteiro,et al.  Iteration-Complexity of Block-Decomposition Algorithms and the Alternating Direction Method of Multipliers , 2013, SIAM J. Optim..

[4]  Bingsheng He,et al.  On the O(1/n) Convergence Rate of the Douglas-Rachford Alternating Direction Method , 2012, SIAM J. Numer. Anal..

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

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

[7]  M. Fortin,et al.  On decomposition - coordination methods using an augmented Lagrangian , 1983 .

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

[9]  R. Glowinski,et al.  Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires , 1975 .

[10]  R. Rockafellar The multiplier method of Hestenes and Powell applied to convex programming , 1973 .

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

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

[13]  D. Luenberger Optimization by Vector Space Methods , 1968 .

[14]  Arthur F. Veinott,et al.  The Supporting Hyperplane Method for Unimodal Programming , 1967, Oper. Res..

[15]  S. Sinha A Duality Theorem for Nonlinear Programming , 1966 .

[16]  Harvey J. Everett Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources , 1963 .

[17]  P. Wolfe A duality theorem for non-linear programming , 1961 .

[18]  J. E. Kelley,et al.  The Cutting-Plane Method for Solving Convex Programs , 1960 .

[19]  W. Fenchel Convex cones, sets, and functions , 1953 .