Restricted simplicial decomposition with side constraints

Abstract

AbstractRestricted 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.