Iterative Methods for Large Scale Convex Optimization
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Date
2017-07
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Publisher
University of Ghana
Abstract
This thesis presents a detailed description and analysis of Bregman’s iterative
method for convex programming with linear constraints. Row and block action
methods for large scale problems are adopted for convex feasibility problems. This
motivates Bregman type methods for optimization.
A new simultaneous version of the Bregman’s method for the optimization of
Bregman function subject to linear constraints is presented and an extension of
the method and its application to solving convex optimization problems is also
made.
Closed-form formulae are known for Bregman’s method for the particular cases of
entropy maximization like Shannon and Burg’s entropies. The algorithms such as
the Multiplicative Algebraic Reconstruction Technique (MART) and the related
methods use closed-form formulae in their iterations. We present a generalization
of these closed-form formulae of Bregman’s method when the objective function
variables are separated and analyze its convergence.
We also analyze the algorithm MART when the problem is inconsistent and give
some convergence results.
Description
Thesis (PhD)
Keywords
Iterative Methods, Large Scale Convex, Optimization