Quasi-Newton algorithms for large scale nonlinear systems

In this work, an evaluation of a number of quasi-Newton algorithms and strategies for sparse, symmetric Hessian matrices was performed. It was shown how these quasi-Newton algorithms could be applied to the unconstrained minimization of a nonlinear function as well as a nonlinear least squares approach to solving a system of nonlinear equations. The best of these algorithms were evaluated for a problem with a fairly large number of degrees of freedom with a large load increment. From this study it is concluded that the proposed quasi-Newton method with the double dogleg strategy and an automatic control on Hessian evaluations is the best algorithm for all of the problems considered in this investigation. The algorithm had no difficulty converging to solutions regardless of the size of the model and regardless of the size of the load or time step. The advantage of being able to take large load or time steps may lie in those problems which involve the location of critical points (limit or bifurcation points) of structures with minimal computational effort. All the algorithms which utilized the double dogleg strategy were consistently better able to converge to the solution - a clear validation of the globally convergent property of the double dogleg strategy. Finally, the usefulness of the double dogleg strategy in solving a system of nonlinear equations via the nonlinear least squares approach and in locating multiple equilibrium configurations using deflation speaks for the versatility of the proposed algorithm. In conclusion, the quasi-Newton algorithm proposed in this dissertation is both robust and efficient for small as well as large scale problems of matrices are exploited. Because sparsity and symmetry the algorithm does not place unreasonable demands on core storage requirements. Furthermore, using the deflation technique with tunneling the algorithm can be extremely useful for post-buckling response studies of structures involving many stable and unstable branches.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Engineering Mechanics

Department dc:contributor.department

Engineering Mechanics

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1983

Author dc:creator

• VandenBrink, Dennis Jay

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10919/101299

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/101299