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Iterative Solution Algorithms for Nonlinear Optimization

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Optimization in Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 120))

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Abstract

Chapter 4 introduces optimality conditions to solve nonlinear programming problems (NLPPs). Optimality conditions have the benefit that they allow us to find all points that are candidate local minima, but can be quite cumbersome. For these reasons, in many practical cases NLPPs are solved using iterative algorithms that are implemented on a computer. In this chapter we begin by first introducing a generic iterative algorithm for solving an unconstrained NLPP. We also introduce two broad approaches to solving constrained NLPPs.

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Notes

  1. 1.

    In practice, software packages often factorize or decompose the Hessian matrix (as opposed to inverting it) to find the Newton’s method direction.

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Author information

Authors and Affiliations

  1. Department of Integrated Systems Engineering, The Ohio State University, Columbus, OH, USA

    Ramteen Sioshansi

  2. Department of Integrated Systems Engineering and Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH, USA

    Antonio J. Conejo

Authors
  1. Ramteen Sioshansi
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  2. Antonio J. Conejo
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Correspondence to Ramteen Sioshansi .

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Sioshansi, R., Conejo, A.J. (2017). Iterative Solution Algorithms for Nonlinear Optimization. In: Optimization in Engineering. Springer Optimization and Its Applications, vol 120. Springer, Cham. https://doi.org/10.1007/978-3-319-56769-3_5

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