This chapter addresses the solution of nonlinear programming (NLP)problemsthrough algorithms whose objective is to find a point satisfying the Karush–Kuhn–Tucker conditions through different applications of Newton's method. The algorithms considered include successive-quadratic programming, reduced-gradient method and interior-point method. The basic assumptions behind each method are stated and used to derive the major steps involved in these algoritms. We make brief reference to optimization software including SNOPT, MINOS, CONOPT, IPOPT and KNITRO. Finally, general guidelines are given how to formulate good NLP models.
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