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Some nonlinear Lagrange and penalty functions for problems with a single constraint

In: Optimization

Author

Listed:
  • J.S. Giri

    (University of Ballarat)

  • A.M. Rubinov†

    (University of Ballarat)

Abstract

We study connections between generalized Lagrangians and generalized penalty functions, which are formed by increasing positively homogeneous functions. In particular we show that the least exact penalty parameter is equal to the least Lagrange multiplier. We also prove, under some natural assumptions, that the natural generalization of a Lagrangian cannot improve it.

Suggested Citation

  • J.S. Giri & A.M. Rubinov†, 2009. "Some nonlinear Lagrange and penalty functions for problems with a single constraint," Springer Optimization and Its Applications, in: Charles Pearce & Emma Hunt (ed.), Optimization, edition 1, chapter 0, pages 41-54, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-98096-6_3
    DOI: 10.1007/978-0-387-98096-6_3
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