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Abstract: We present an approach for solving optimization problems in which the variables are distributed among p processors. Each processor has primary responsibility for updating its own block of variables in parallel while allowing the remaining variables to change in a restricted fashion (e. g. along a steepest descent, quasi--Newton, or any arbitrary direction). This "forget-me-not" approach is a distinctive feature of our algorithm which has not been analyzed before. The parallelization step is... (Update)
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...algorithm when coordination is performed as in Step 2 and the minimization in Step 1 is exact is an application of Theorem 3. 6 of Ferris Mangasarian (1993). The following proposition gives the formal statement of this result. Proposition 8 If F 2 LC 1 M (R n1 n2 : nK )...
.... such as: the Dantzig Wolfe decomposition [19] the Schultz Meyer shifted barrier 6 method [92] the Parallel Variable Distribution [33], and Parallel Constraint Distribution [32] algorithms of Ferris and Mangasarian, and the Diagonal Quadratic Approximation method of Mulvey...
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BibTeX entry: (Update)
M. C. Ferris and O. L. Mangasarian, Parallel variable distribution, SIAM J. Optimization 4(1994) 815-832. http://citeseer.ist.psu.edu/article/ferris94parallel.html More
@techreport{ ferris93parallel,
author = "Michael C. Ferris and Olvi L. Mangasarian",
title = "Parallel Variable Distribution",
number = "CS-TR-1993-1175",
year = "1993",
url = "citeseer.ist.psu.edu/article/ferris94parallel.html" }
Citations (may not include all citations):482 Iterative Solution of Nonlinear Equations in Several Variabl.. (context) - Ortega, Rheinboldt - 1970
197 Constrained Optimization and Lagrange Multiplier Methods (context) - Bertsekas - 1982
175 Parallel and Distributed Computation (context) - Bertsekas, Tsitsiklis - 1989
172 Nonlinear Programming: Sequential Unconstrained Minimization.. (context) - Fiacco, McCormick - 1968
149 CUTE: Constrained and unconstrained testing environment - Bongartz, Conn et al. - 1993
119 Nonlinear Programming (context) - Mangasarian - 1969
74 Computer Science Department (context) - Culler, Programming
72 Minimization of functions having Lipschitz-continuous first .. (context) - Armijo - 1966
53 CMMD Reference Manual (context) - Corporation, MA - 1993
38 Technical Report SOL (context) - Murtagh, Saunders et al. - 1983
33 Naval Research Logistics Quarterly (context) - Frank, Wolfe et al. - 1956
27 Numerical Analysis (context) - Ortega - 1972
11 The gap function of a convex program (context) - Hearn - 1982
11 Parallel gradient distribution in unconstrained optimization - Mangasarian - 1993
9 Minimum principle sufficiency (context) - Ferris, Mangasarian - 1992
7 A dual differentiable exact penalty function (context) - Han, Mangasarian - 1983
7 Augmented Lagrange multiplier functions and duality in nonco.. (context) - Rockafellar - 1974
6 Dual coordinate ascent methods for non--strictly convex mini.. (context) - Tseng - 1993
1 Computer Sciences Department Technical Report (context) - Bennett, Mangasarian et al. - 1993
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