Math 2.0

Operations research, mathematical programming Basic notions of optimization Concept

Constrained optimisation

Builds on Function of several variablesLocal maximum and minimum

Summary

Constrained optimisation looks for the maximum or minimum of an objective function ff of several variables over the set of points that satisfy given constraints. Typical constraints are equations gi(x)=cig_i(x) = c_i and inequalities hj(x)≥djh_j(x) \ge d_j.

Remarks

An example is to maximise f(x,y)=xyf(x, y) = x y on the circle x2+y2=2x^2 + y^2 = 2. The maximum value is 11, at (1,1)(1, 1) and (−1,−1)(-1, -1). For equality constraints, one method solves the constraints for some variables and substitutes them into ff. Another method uses Lagrange multipliers. A constrained extremum need not be a critical point of ff. In the example above, ∇f(1,1)=(1,1)≠0\nabla f(1, 1) = (1, 1) \ne 0.

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  1. Euclidean space object
  2. Function concept
  3. Function of several variables concept
  4. Local maximum and minimum concept
  5. Constrained optimisation concept

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2 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Constrained_optimization, General form
  2. Web https://en.wikipedia.org/wiki/Constrained_optimization, Equality constraints
About this page
Tag0EPW94MJ1P
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Aliasesconstrained-optimization
Kindconcept
WritingW0 stub
MSC90C30
UsesFunction of several variables, Local maximum and minimum
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