# Solving structure optimization with Lagrange duality

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1. Nov 8, 2014

### ENgez

1. The problem statement, all variables and given/known data
I need to optimize the following structure with respect to compliance $P\cdot u_y$. the constraint is that the volume of the truss must not exceed $V_0$. The design variables are the bar cross sections $A_1,A_2,A_3$

2. Relevant equations
The mathematical programming problem I got is:

3. The attempt at a solution
The book wants me to solve this with both KKT conditions and lagrange duality.
Applying the KKT conditions leads to a set of 4 non linear equations that are complicated but solvable for the optimal design variables.

What i don't understand is how to use the Lagrange duality to solve this problem. As i understand, it is supposed to be easier to apply to more complex structural optimization problems, such as this indeterminate truss.

The book only shows how to use the Lagrange duality for separable programming problems, but my objective function is non separable, so how do I go about it?

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2. Nov 13, 2014