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

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  • Chin How Jeffrey Pang

    (National University of Singapore)

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.

Suggested Citation

  • Chin How Jeffrey Pang, 2019. "Dykstra’s Splitting and an Approximate Proximal Point Algorithm for Minimizing the Sum of Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1019-1049, September.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:3:d:10.1007_s10957-019-01512-z
    DOI: 10.1007/s10957-019-01512-z
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    References listed on IDEAS

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