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Projection methods for minimizing a finite sum of convex functions

Hold Date
2018-05-22 12:00〜2018-05-22 13:00
Lecture Room S W1-C-503, West Zone 1, Ito campus, Kyushu University
Object person
Hong-Kun XU (Department of Mathematics, Hangzhou Dianzi University, China)

Many applied problems are formulated as a minimization problem where the objective function is a finite sum of convex functions and the constraint set is the intersection of finitely many closed convex sets. In this talk we will discuss projection methods, including sequential, parallel, and cyclic projection algorithms, for solving these sort of optimization problems. These algorithms consist of two steps. The first step is an inner circle of gradient descent process to be executed through each component function and the second step is a projection process that is applied to produce the next iterate. These algorithms are proved to converge to the optimal value of the objective function by assuming boundedness of the gradients at the iterates of the component functions and the stepsizes being diminishing. It is however unknown if the iterates of the algorithms can fully converge to an optimal solution.