I model a structure in Ansys and I want to make optimization and I think I can use Levenberg-Marquardt for optimization purpose. But I don't know how and what is the theory behind it.
There is several optimization Software that can interface with ANSYS, like OptiSLang. Or you could write a script in Matlab using the Optimization Toolbox that calls ANSYS in Batch mode. Which is the algorithm best suited really depends on the problem. I had good experience with genetic algorithms for optimization problems where a CAE model is in the loop.