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
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
CDR, C (2021). Iterative Methods for Large Scale Convex Optimization. Afribary.com: Retrieved April 15, 2021, from https://afribary.com/works/iterative-methods-for-large-scale-convex-optimization
Coalition, CDR. "Iterative Methods for Large Scale Convex Optimization" Afribary.com. Afribary.com, 02 Apr. 2021, https://afribary.com/works/iterative-methods-for-large-scale-convex-optimization . Accessed 15 Apr. 2021.
Coalition, CDR. "Iterative Methods for Large Scale Convex Optimization". Afribary.com, Afribary.com, 02 Apr. 2021. Web. 15 Apr. 2021. < https://afribary.com/works/iterative-methods-for-large-scale-convex-optimization >.
Coalition, CDR. "Iterative Methods for Large Scale Convex Optimization" Afribary.com (2021). Accessed April 15, 2021. https://afribary.com/works/iterative-methods-for-large-scale-convex-optimization