Question

1. Solve the following minimization optimization problem using KKT. Minimize f(x1, x2, x3) = (x1 - 1)^2 + 2(x2 + 2)^2 + 3(x3 - 3)^2 + x1x2 + 2x1x3 + 3x2x3 Subject to g1(x1, x2, x3) = x1 - x2 - 2x3 <= 12 g2(x1, x2, x3) = x1 + 2x2 - 3x3 <= 8 For this question, you will need to solve sets of simultaneous equations. Under no circumstances do this by hand! You should use Excel (I'll explain this later in one of the lectures) or MATLAB to solve systems of simultaneous equations. You must however show what the equations that you are solving are, and then state the method used to solve them (e.g. Excel or MATLAB) and clearly state the answers.

          1. Solve the following minimization optimization problem using KKT.
Minimize f(x1, x2, x3) = (x1 - 1)^2 + 2(x2 + 2)^2 + 3(x3 - 3)^2 + x1x2 + 2x1x3 + 3x2x3
Subject to g1(x1, x2, x3) = x1 - x2 - 2x3 <= 12
g2(x1, x2, x3) = x1 + 2x2 - 3x3 <= 8

For this question, you will need to solve sets of simultaneous equations. Under no circumstances do this by hand! You should use Excel (I'll explain this later in one of the lectures) or MATLAB to solve systems of simultaneous equations. You must however show what the equations that you are solving are, and then state the method used to solve them (e.g. Excel or MATLAB) and clearly state the answers.

1. Solve the following minimization optimization problem using KKT.
Minimize f(x1, x2, x3) = (x1 - 1)^2 + 2(x2 + 2)^2 + 3(x3 - 3)^2 + x1x2 + 2x1x3 + 3x2x3
Subject to g1(x1, x2, x3) = x1 - x2 - 2x3 <= 12
g2(x1, x2, x3) = x1 + 2x2 - 3x3 <= 8

For this question, you will need to solve sets of simultaneous equations. Under no circumstances do this by hand! You should use Excel (I'll explain this later in one of the lectures) or MATLAB to solve systems of simultaneous equations. You must however show what the equations that you are solving are, and then state the method used to solve them (e.g. Excel or MATLAB) and clearly state the answers.

Added by Allison P.

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