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Title: A penalty/modified barrier method for large-scale quadratic programming
Author: Brooks, S. A.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2000
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The tools for solving large-scale sparse Quadratic Programming (QP) problems have many applications. They can be used to solve naturally occurring problems, which arise in engineering, economics, etc, or they can be used as part of a Sequential Quadratic Programming (SQP) structure for solving non-linear programming problems. The performance of SQP methods depends greatly on the QP solver, and for this reason the development and implementation of an efficient QP method is of paramount importance. In this work we consider the application of the Penalty/Modified Barrier Function (PE/MBF) method in the solution of large-scale Quadratic Programming problems. We consider using "hot starts" to initialise the parameters for one problem using information based on a related solved problem. The limitations of the Classical Barrier Function (CBF) method are discussed and then it is shown how the CBF can be used to initialise the Lagrange multipliers associated with a Modified Barrier Function. Numerical results showed that this is effective in reducing the number of iterations to convergence. The Newton strategy developed in this work exploits both the sparsity of the problem under consideration and the symmetry of the Hessian matrix. We consider the convergence rates of the Lagrange multipliers. In particular, we show that, in practice the Lagrange multipliers corresponding to inactive constraints converge faster than those corresponding to active constraints. We give a procedure for predicting the active constraints. Numerical results confirm its effectiveness.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available