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A decomposition procedure based on approximate newton directions

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  • Conejo, Antonio J.
  • Nogales Martín, Francisco Javier
  • Prieto Fernández, Francisco Javier

Abstract

The efficient solution of large-scale linear and nonlinear optimization problems may require exploiting any special structure in them in an efficient manner. We describe and analyze some cases in which this special structure can be used with very little cost to obtain search directions from decomposed subproblems. We also study how to correct these directions using (decomposable) preconditioned conjugate gradient methods to ensure local convergence in all cases. The choice of appropriate preconditioners results in a natural manner from the structure in the problem. Finally, we conduct computational experiments to compare the resulting procedures with direct methods, as well as to study the impact of different preconditioner choices.

Suggested Citation

  • Conejo, Antonio J. & Nogales Martín, Francisco Javier & Prieto Fernández, Francisco Javier, 2001. "A decomposition procedure based on approximate newton directions," DES - Working Papers. Statistics and Econometrics. WS ws010906, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws010906
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    1. Stein W. Wallace & Stein-Erik Fleten, 2002. "Stochastic programming in energy," GE, Growth, Math methods 0201001, University Library of Munich, Germany, revised 13 Nov 2003.
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    1. Pan, Zhaoguang & Guo, Qinglai & Sun, Hongbin, 2017. "Feasible region method based integrated heat and electricity dispatch considering building thermal inertia," Applied Energy, Elsevier, vol. 192(C), pages 395-407.

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