How to optimize a matrix with 4 parameters

Hi Guys!

I could use some help optimizing a stiffness matrix for eigenvalue analysis.

I would like to optimize a (polynomial) eigenvalue problem for a given Mass matrix M and a varying Stiffness matrix K. The stiffnessmatrix is calculated with 4 varying parameters and I would like to calculate the ideal combination for a certain output of eigenvalues.

Problem:

Given matrix M (12X12) Varying Stiffness matrix K (12X12), dependent on parameters A,B,C,D

A=0:1:10

B=0:1:10

C=0:1:10

D=0:1:10

Eigen=imag(polyeig(K,zeros(12),M))

This would return 10x10x10x10= 10000 combinations

I would like the values or a selection of the values in the Eigen vector to be lower or equal to a certain value X.

The script or function should return to me the optimized values of A,B,C,D for Eigen =< X

Any ideas on the correct approach to solve this problem?

[Matt J]

What is the objective function being optimized? Eigen appears to be a constraint function. Also 10000 combinations doesn't seem that large. Why not just use exhaustive search?