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    A New Interpolation Approach for Linearly Constrained Convex Optimization

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    MSc Thesis Francisco Javier Franco.pdf
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    Type
    Thesis
    Authors
    Espinoza, Francisco
    Advisors
    Rockwood, Alyn
    Committee members
    Turkiyyah, George
    Zhang, Xiangliang cc
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2012-08
    Permanent link to this record
    http://hdl.handle.net/10754/244891
    
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    Abstract
    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-F8YJX
    DOI
    10.25781/KAUST-F8YJX
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-F8YJX
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; MS Theses; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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