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LAGRANGE MULTIPLIER

LAGRANGE MULTIPLIER. BY ENI SUMARMININGSIH, SSI, MM. Constained Optimization. “Constrained Optimization” involves the optimization of a process subject to constraints. Constraints have two basic types — Equality Constraints -- some factors have to equal constraints

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LAGRANGE MULTIPLIER

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  1. LAGRANGE MULTIPLIER BY ENI SUMARMININGSIH, SSI, MM

  2. Constained Optimization “Constrained Optimization” involves the optimization of a process subject to constraints. Constraints have two basic types — Equality Constraints -- some factors have to equal constraints — Inequality Constraints -- some factors have to be less less than or greater than the constraints (these are “upper” and “lower” bounds

  3. Equality Constraints Subject to (s.t.): Total costs = Budget = p1x1 + p2x2

  4. APPROACH In this case, transform optimization of a “constrained” situation to optimization of “unconstrained” situation

  5. Shadow Prices Shadow Price is the Rate of change of objective function per unit change of constraint This is meaning of Lagrangean multiplier

  6. Let’s see how this works in example, by changing constraint by 0.1 units:

  7. SOAL -SOAL 1. Minimize f(x) = + S.t. 2. Minimize + s.t 3. Minimize s.t.

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