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Methods for Nonlinearly Constrained Problems

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Nonlinear Optimization

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 282))

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.

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Authors and Affiliations

  1. Faculty of Management, University of New Brunswick, Fredericton, NB, Canada

    H. A. Eiselt

  2. Department of Industrial Engineering, Dalhousie University, Halifax, NS, Canada

    Carl-Louis Sandblom

Authors
  1. H. A. Eiselt
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  2. Carl-Louis Sandblom
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Eiselt, H.A., Sandblom, CL. (2019). Methods for Nonlinearly Constrained Problems. In: Nonlinear Optimization . International Series in Operations Research & Management Science, vol 282. Springer, Cham. https://doi.org/10.1007/978-3-030-19462-8_7

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