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Parallel computing tests on large-scale convex optimization

  • Markku Kallio
  • Seppo Salo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1541)

Abstract

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 [1].

Keywords

Convex Optimization Gradient Evaluation Large Scale Optimization Algebraic Step Linear Programming Test 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Katja Ainassaari, Markku Kallio and Antero Ranne, “An Asset Management Model for a Pension Insurance Company,” Helsinki School of Economics, 1997.Google Scholar
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    M. S. Bazaraa, C. M. Shetty, Nonlinear Programming, John Wiley & Sons, 1979.Google Scholar
  3. 3.
    Markku Kallio and Charles H. Rosa, “Large-Scale Optimization via Saddle Point Computation,” Operations Research (forthcoming).Google Scholar
  4. 4.
    Markku Kallio and Seppo Salo, “Tatonnement Procedures for Linearly Constrained Convex Optimization,” Management Science Vol. 40, pages 788–797, 1994.zbMATHCrossRefGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Markku Kallio
    • 1
  • Seppo Salo
    • 1
  1. 1.Helsinki School of EconomicsHelsinkiFinland

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