A New Interpolation Approach for Linearly Constrained Convex Optimization
Name:
MSc Thesis Francisco Javier Franco.pdf
Size:
2.939Mb
Format:
PDF
Description:
PDF file
Type
ThesisAuthors
Espinoza, FranciscoAdvisors
Rockwood, AlynCommittee members
Turkiyyah, GeorgeZhang, Xiangliang

Date
2012-08Permanent link to this record
http://hdl.handle.net/10754/244891
Metadata
Show full item recordAbstract
In this thesis we propose a new class of Linearly Constrained Convex Optimization methods based on the use of a generalization of Shepard's interpolation formula. We prove the properties of the surface such as the interpolation property at the boundary of the feasible region and the convergence of the gradient to the null space of the constraints at the boundary. We explore several descent techniques such as steepest descent, two quasi-Newton methods and the Newton's method. Moreover, we implement in the Matlab language several versions of the method, particularly for the case of Quadratic Programming with bounded variables. Finally, we carry out performance tests against Matab Optimization Toolbox methods for convex optimization and implementations of the standard log-barrier and active-set methods. We conclude that the steepest descent technique seems to be the best choice so far for our method and that it is competitive with other standard methods both in performance and empirical growth order.Citation
Espinoza, F. (2012). A New Interpolation Approach for Linearly Constrained Convex Optimization. KAUST Research Repository. https://doi.org/10.25781/KAUST-F8YJXae974a485f413a2113503eed53cd6c53
10.25781/KAUST-F8YJX