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Volume 4, Issue 2, 1 August 2022, Pages 245-271
Abstract. The convex optimization has been used for modeling of many estimation problems in data science and engineering, where convex constraint sets in such a model express respectively a priori knowledge regarding a certain unknown vector to be estimated. The LiGME model was established recently in [J. Abe, M. Yamagishi, I. Yamada, Linearly involved generalized Moreau enhanced models and their proximal splitting algorithm under overall convexity condition, Inverse Probl. 36 (2020), 035012] for a sound utilization of linearly involved regularizers closer to certain ideal discrete measures, for sparsity as well as for low-rankness, than their convex envelopes. Despite of the nonconvexity of linearly involved regularizers, the LiGME model can keep the overall convexity of its optimization model with a strategic parameter tuning. In this paper, for flexible exploitation of multiple convex constraint sets, we propose a constrained LiGME (cLiGME) model as an enhancement of the original LiGME model. Within the frame of convex optimization, the proposed cLiGME model can promote such desired features more strategically than standard models using convex regularizers, as well as can admit multiple linearly involved convex indicator functions for hard constraints. We also propose a proximal splitting type algorithm for the cLiGME model and demonstrate its effectiveness with a simple numerical experiment. The cLiGME model can be seen as an integration of central ideas in the LiGME model and the set theoretic estimation.
How to Cite this Article:
W. Yata, M. Yamagishi, I. Yamada, A constrained LiGME model and its proximal splitting algorithm under overall convexity condition, J. Appl. Numer. Optim. 4 (2022), 245-271.