MathLiveLagrange multiplier condition
At a constrained extremum of f subject to g = 0, the gradient of f is parallel to the gradient of g, with the scalar λ as the proportionality factor. It is used to find maxima and minima of a function under an equality constraint.
\nabla f(x,y) = \lambda \nabla g(x,y)What the symbols mean
| objective function being optimized | |
| constraint function, with the feasible set given by g(x,y)=0 | |
| Lagrange multiplier, a scalar | |
| gradient operator with respect to x and y |
About this formula
- FieldMathematics
- TopicOptimization
- LevelUniversity
- Also calledLagrange multipliers, method of Lagrange multipliers, constrained optimization Lagrange, Lagrangian stationary condition, undetermined multiplier, optimization with constraint
- SourceWikidata Q598870
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