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MATH
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Definitions from Constrained extrema

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Constrained extremum

Let ff be an objective function and let

C={(x,y):g(x,y)=0}C=\{(x,y):g(x,y)=0\}

be its feasible set. A constrained maximum or minimum of ff is a maximum or minimum of ff when the comparison is restricted to points in CC.

The constraint limits the directions in which we may move. A point can fail to be an unconstrained stationary point and still be a constrained extremum, because the directions in which ff would increase or decrease are not feasible.

  1. [1]:Lagrange multipliers
  2. [2]:Minimise a distance through its square

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Constrained extremum