Dykstra’s Splitting and an Approximate Proximal Point Algorithm for Minimizing the Sum of Convex Functions

Chin How Jeffrey Pang ()
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Chin How Jeffrey Pang: National University of Singapore

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 3, No 9, 1019-1049

Abstract: Abstract We show that Dykstra’s splitting for projecting onto the intersection of convex sets can be extended to minimize the sum of convex functions and a regularizing quadratic function. We give conditions for which convergence to the primal minimizer holds so that more than one convex function can be minimized at a time, the convex functions are not necessarily sampled in a cyclic manner, and the SHQP strategy for problems involving the intersection of more than one convex set can be applied. When the sum does not involve the regularizing quadratic function, we discuss an approximate proximal point method combined with Dykstra’s splitting to minimize this sum.

Keywords: Dykstra’s splitting; Proximal point algorithm; Block coordinate minimization; 90C25; 65K05; 68Q25; 47J25 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01512-z

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