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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

LAGRANGE MULTIPLIER

BY ENI SUMARMININGSIH, SSI, MM


Constained optimization
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


Equality constraints
Equality Constraints

Subject to (s.t.):

Total costs = Budget = p1x1 + p2x2


Approach
APPROACH

In this case, transform optimization of a

“constrained” situation to optimization of

“unconstrained” situation


Shadow prices
Shadow Prices

Shadow Price is the Rate of change of objective function per unit change of constraint

This is meaning of Lagrangean multiplier


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


Soal soal
SOAL -SOAL

1. Minimize f(x) = +

S.t.

2. Minimize +

s.t

3. Minimize

s.t.


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