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Methods for Nonlinearly Constrained Problems

In: Nonlinear Optimization

Author

Listed:
  • H. A. Eiselt

    (University of New Brunswick)

  • Carl-Louis Sandblom

    (Dalhousie University)

Abstract

As opposed to the previous chapter, the methods presented in this chapter allow the given constraints to be nonlinear. In the first section of this chapter, we consider problems with convex constraints, starting with the cutting plane method for nonlinear programming due to Kelley (1960). Although Kelley’s method suffers from a numerically slow convergence in comparison with other methods (except possibly for highly nonlinear constraints), we cover it here because of the considerable theoretical interest of the cutting plane principle. We continue with the generalized reduced gradient (GRG) method, which may be regarded as a standard technique for convex differentiable programming. Techniques for handling nondifferentiable functions using subgradients as well as methods for concave objective functions are then described.

Suggested Citation

  • H. A. Eiselt & Carl-Louis Sandblom, 2019. "Methods for Nonlinearly Constrained Problems," International Series in Operations Research & Management Science, in: Nonlinear Optimization, chapter 0, pages 243-278, Springer.
    • Handle: RePEc:spr:isochp:978-3-030-19462-8_7
    DOI: 10.1007/978-3-030-19462-8_7
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