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Applied Optimization by Ross Baldick

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9

Case studies of unconstrained optimization

In this chapter we will introduce two case studies:

(i)   multi-variate linear regression (Section 9.1), and

(ii)   state estimation in an electric power system (Section 9.2).

Both problems will turn out to be unconstrained optimization problems of the special class of least-squares data fitting problems [84, chapter 13].

9.1 Multi-variate linear regression

Some of this section is based on [103] and further details can be found there. The development assumes a background in probability. See, for example, [31, 103].

9.1.1 Motivation

In many applications, we have a hypothesized functional relationship between variables. That is, we believe that there are some dependent variables that vary according to ...

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