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ClueBot NG (talk | contribs) m Reverting possible vandalism by 49.169.220.7 to version by LPS and MLP Fan. Report False Positive? Thanks, ClueBot NG. (3706772) (Bot) |
→Substitution method: g(x) → p(x); \frac{\partial g}{\partial x} → \frac{\partial p}{\partial x} {objective: to prevent confusion of the interpretation here as an adapted cost function with the interpretation in an equality constraint for g intended elsewhere in the article } |
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===Equality constraints===
====Substitution method====
For very simple problems, say a function of two variables subject to a single equality constraint, it is most practical to apply the method of substitution.<ref>{{cite book |first=Mike |last=Prosser |title=Basic Mathematics for Economists |___location=New York |publisher=Routledge |year=1993 |isbn=0-415-08424-5 |chapter=Constrained Optimization by Substitution |pages=338–346 }}</ref> The idea is to substitute the constraint into the objective function to create a [[Function composition|composite function]] that incorporates the effect of the constraint. For example, assume the objective is to maximize <math>f(x,y) = x \cdot y</math> subject to <math>x + y = 10</math>. The constraint implies <math>y = 10 - x</math>, which can be substituted into the objective function to create <math>
====Lagrange multiplier====
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