Static Minimization of Himmelblau's Funcition

Computer Methods in Chemical Engineering

Problem Statement: Find the minima of the following function. 

  Minimize L(x,y) = (x2+y-11)2 + (x+y2-7)2
subject to the following constraints
  1. Case I. no equality nor inequality constraints
  2. Case II. -x+y+6≤0 & -x-y≤0

Solution:

With no constraints, there are four equally valid solutions, each resulting in an identical value for L (L=0). The four points are: 

  1. x=-3.779, y=-3.283
  2. x=-2.805, y=-3.131
  3. x= 3,     y= 2
  4. x= 3.584, y=-1.848
With the specified equality constraints, it turns out that only one of them is effective. The minimum value of L is 3.96, which happens at: 
  x= 3.744, y=-2.257

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Computer Methods in Chemical Engineering -- Static Minimization of Himmelblau's Funcition
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