A structured reduced sequential quadratic programming and its application to a shape design problem
|dc.description.abstract||The objective of this work is to solve a model one dimensional duct design problem
using a particular optimization method. The design problem is formulated as an equality
constrained optimization, called All at once method, so that the analysis problem is not
solved until the optimal design is reached. Furthermore, the block structure in the Jacobian
of the linearized constraints is exploited by decomposing the variables into the design and
flow parts. To achieve this, Sequential quadratic programming with BFGS update for
the reduced Hessian of the Lagrangian function is used with Variable reduction method
which preserves the structure of the Jacobian in representing the null space basis matrix.
By updating the reduced Hessians only of which the dimension is the number of design
variables, the storage requirement for Hessians is reduced by a large amount. In addition,
the flow part of the Jacobian can be computed analytically.
The algorithm with a line search globalization is described. A global and local analysis is provided with a modification of the paper by Byrd and Nocedal [Mathematical Programming 49(1991) pp 285-323] in which they analyzed the similar algorithm with the Orthogonal factorization method which assumes the orthogonality of the null space basis matrix. Numerical results are obtained and compared favorably with results from the Black box method - unconstrained optimization formulation.
|dc.title||A structured reduced sequential quadratic programming and its application to a shape design problem||en_US|
|thesis.degree.grantor||Virginia Polytechnic Institute and State University||en_US|
|dc.contributor.committeechair||Herdman, Terry L.||en_US|
|dc.contributor.committeemember||Burns, John A.||en_US|
|dc.contributor.committeemember||Cliff, Eugene M.||en_US|
|dc.contributor.committeemember||Gunzburger, Max D.||en_US|
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