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Journal of Optimization Theory and Applications

, Volume 55, Issue 2, pp 313–326 | Cite as

Scheduling of power generation via large-scale nonlinear optimization

  • P. P. J. Van Den Bosch
  • F. A. Lootsma
Contributed Papers

Abstract

We investigate methods for solving high-dimensional nonlinear optimization problems which typically occur in the daily scheduling of electricity production: problems with a nonlinear, separable cost function, lower and upper bounds on the variables, and an equality constraint to satisfy the demand. If the cost function is quadratic, we use a modified Lagrange multiplier technique. For a nonquadratic cost function (a penalty function combining the original cost function and certain fuel constraints, so that it is generally not separable), we compare the performance of the gradient-projection method and the reduced-gradient method, both with conjugate search directions within facets of the feasible set. Numerical examples at the end of the paper demonstrate the effectiveness of the gradient-projection method to solve problems with hundreds of variables by exploitation of the special structure.

Key Words

Dispatch problems continuous knapsack problems Lagrange multiplier technique gradient projection reduced gradients conjugate directions 

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Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • P. P. J. Van Den Bosch
    • 1
  • F. A. Lootsma
    • 2
  1. 1.Department of Electrical EngineeringDelft University of TechnologyDelftHolland
  2. 2.Department of Mathematics and InformaticsDelft University of TechnologyDelftHolland

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