Finiteness in restricted simplicial decomposition

Authors:
D.W Hearn;S Lawphongpanich;J.A Ventura
Affiliations:
Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA;Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA;Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA
Venue:
Operations Research Letters
Year:
1985

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Abstract

Simplicial decomposition is an important form of decomposition for large non-linear programming problems with linear constraints. Von Hohenbalken has shown that if the number of retained extreme points is n + 1, where n is the number of variables in the problem, the method will reach an optimal simplex after a finite number of master problems have been solved (i.e., after a finite number of major cycles). However, on many practical problems it is infeasible to allocate computer memory for n + 1 extreme points. In this paper, we present a version of simplicial decomposition where the number of retained extreme points is restricted to r, 1 =