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Penalty and Barrier Methods

In: Linear and Nonlinear Programming

Author

Listed:
  • David G. Luenberger

    (Stanford University)

  • Yinyu Ye

    (Stanford University)

Abstract

Penalty and barrier methods are procedures for approximating constrained optimization problems by unconstrained problems. The approximation is accomplished in the case of penalty methods by adding to the objective function a term that prescribes a high cost for violation of the constraints, and in the case of barrier methods by adding a term that favors points interior to the feasible region over those near the boundary. Associated with these methods is a parameter c or μ that determines the severity of the penalty or barrier and consequently the degree to which the unconstrained problem approximates the original constrained problem. For a problem with n variables and m constraints, penalty and barrier methods work directly in the n-dimensional space of variables, as compared to primal methods that work in (n − m)-dimensional space.

Suggested Citation

  • David G. Luenberger & Yinyu Ye, 2016. "Penalty and Barrier Methods," International Series in Operations Research & Management Science, in: Linear and Nonlinear Programming, edition 4, chapter 0, pages 397-428, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-18842-3_13
    DOI: 10.1007/978-3-319-18842-3_13
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