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Extended Lagrange and Penalty Functions in Optimization

Author

Listed:
  • A. M. Rubinov

    (University of Ballarat)

  • X. Q. Yang

    (Hong Kong Polytechnic University)

  • B. M. Glover

    (Curtin University of Technology)

Abstract

We consider nonlinear Lagrange and penalty functions for optimization problems with a single constraint. The convolution of the objective function and the constraint is accomplished by an increasing positively homogeneous of the first degree function. We study necessary and also sufficient conditions for the validity of the zero duality gap property for both Lagrange and penalty functions and for the exact penalization. We also study the so-called regular weak separation functions.

Suggested Citation

  • A. M. Rubinov & X. Q. Yang & B. M. Glover, 2001. "Extended Lagrange and Penalty Functions in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 381-405, November.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:2:d:10.1023_a:1011938519299
    DOI: 10.1023/A:1011938519299
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    References listed on IDEAS

    as
    1. C. J. Goh & X. Q. Yang, 2001. "Nonlinear Lagrangian Theory for Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 109(1), pages 99-121, April.
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