Methods for Nonlinearly Constrained Problems

H. A. Eiselt and Carl-Louis Sandblom
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H. A. Eiselt: University of New Brunswick
Carl-Louis Sandblom: Dalhousie University

Chapter Chapter 7 in Nonlinear Optimization, 2019, pp 243-278 from Springer

Abstract: 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.

Date: 2019
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DOI: 10.1007/978-3-030-19462-8_7

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