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 Cray 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 .
KeywordsConvex Optimization Gradient Evaluation Large Scale Optimization Algebraic Step Linear Programming Test
Unable to display preview. Download preview PDF.
- 1.Katja Ainassaari, Markku Kallio and Antero Ranne, “An Asset Management Model for a Pension Insurance Company,” Helsinki School of Economics, 1997.Google Scholar
- 2.M. S. Bazaraa, C. M. Shetty, Nonlinear Programming, John Wiley & Sons, 1979.Google Scholar
- 3.Markku Kallio and Charles H. Rosa, “Large-Scale Optimization via Saddle Point Computation,” Operations Research (forthcoming).Google Scholar
- 5.Netlib, LP Test Problems, Bell Laboratories.Google Scholar
- 6.B.A. Murtagh and M.A. Saunders, MINOS—A Modular In-core Nonlinear Optimization System, Version 5.4, Stanford University, 1993.Google Scholar
- 7.R.T. Rockafellar, Convex Analysis, Princeton University Press, 1970.Google Scholar