**12**

Case studies of equality-constrained optimization

In this chapter we will introduce two case studies:

(i) production, at least-cost, of a commodity from machines, while meeting a total demand (Section 12.1), and

(ii) state estimation in an electric power system where the power injections at some of the buses are known to high accuracy (Section 12.2).

Both problems will turn out to be equality-constrained optimization problems. The first will introduce several new ideas in problem formulation, while the second will build on the state estimation case study from Section 9.2.

**12.1 Least-cost production**

**12.1.1 Motivation**

Consider a machine that makes a certain product, requiring some costly input to produce. In many industries it is possible ...

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