Parallel computing tests on large-scale convex optimization

Large scale optimization models have traditionally been a valuable tool for management within the private sector and government. Their use has ranged from planning of investments over long horizons, to scheduling of day-to-day operations. Applications involving dynamics and uncertainty, e.g. in finance, often result in models of very large scale. Using Gray T3E parallel computer, we test a new solution technique for a general class of large convex optimization models with differentiable objective and constraint functions. The method is based on saddle point computation of the standard Lagrangian. The algorithm possesses a variety of beneficial characteristics, such as a structure that makes it amenable to parallelization, and no requirement that large systems of equations be solved. We demonstrate the approach using the largest linear programming problem stocfor3 of the test problem library, as well as several versions of a nonlinear multi-stage stochastic optimization model. The former is a forestry planning model. The latter was developed for risk management in a pension insurance company [1].