Novel insights into the multiplier rule
2005-09-29
Research Paper
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We present the Lagrange multiplier rule, one of the basic optimization methods, in a new way. Novel features include: • Explanation of the true source of the power of the rule: reversal of tasks, but not the use of multipliers. • A natural proof based on a simple picture, but not the usual technical derivation from the implicit function theorem. • A practical method to avoid the cumbersome second order conditions. • Applications from various areas of mathematics, physics, economics. • Some hnts on the use of the rule.
Keywords
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- point
- example
- problem
- lagrange multiplier rule
- solution
- multiplier
- function
- equation
- variable
- lagrange
- triangle
- proof
- multiplier rule
- constraint
- value
- theorem
- angle
- x 1 |
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- inequality
