Three stepsize strategies are considered for Sequential Quadratic Programming and Primal-Dual Interior Point methods. Each strategy has its advantages and disadvantages. Switch rules are implemented, that combine all three strategies so as to complement their merits and avoid their drawbacks. Both algorithms are proven to converge to a local minimum from arbitrary starting points, yielding gl.obal convergence. In addition, it is shown that unity stepsizes are achieved. Consequently, superlinear convergence is maintained. Also, the penalty parameter is updated finitely often, which thereby avoids numerical difficulties. Promising results on small and larger scale problems validate the global and superlinear convergence properties of the algorithms and also display that the value of the penalty parameter is kept low at all times. Finally, the algorithms are used as building blocks for solving Mixed Integer Nonlinear Programming probl~ms using the Generalized Benders Decomposition and the Generalized Outer Approximation.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:504757 |
| Date | January 2007 |
| Creators | Tzallas-Regas, George |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
Page generated in 0.0086 seconds