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Restricted simplicial decomposition with side constraints
Author(s) -
Marín ÁNgel
Publication year - 1995
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230260405
Subject(s) - simplex , simplex algorithm , mathematical optimization , decomposition , mathematics , iterated function , set (abstract data type) , nonlinear system , intersection (aeronautics) , convergence (economics) , linear programming , algorithm , computer science , combinatorics , ecology , mathematical analysis , physics , quantum mechanics , economic growth , engineering , economics , biology , programming language , aerospace engineering
Restricted Simplicial Decomposition with Side Constraints is a price decomposition method designed for large‐scale nonlinear problems with a set of linear constraints with special structure and an additional set of linear side constraints. The resultant algorithm iterates by solving a linear subproblem subject to the set of structured constraints and a small nonlinear master problem whose feasible region is defined by the intersection of a simplex and the set of side constraints. The number of variables of the master problem is controlled by a parameter named r. The conditions required for the parameter r and the rules for dropping extreme points of the simplex are established for global convergence of the algorithm. Computational results are presented for nonlinear network problems with side constraints.