Journal Article

Dr Hoa Bui

Authors: Hoa T. Bui* Regina S. Burachik† Evgeni A. Nurminski‡ Matthew K. Tam



arXiv preprint arXiv:2207.10879 (2022).

October 21, 2022

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In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those established for the linear programming setting in Nurminski (2015) by considering problems that: (1) may have multiple solutions, (2) do not satisfy strict complementary conditions, and (3) possess non-linear convex constraints. As a by-product of our analysis, we provide a quantitative estimate on the required distance between the infeasible point and the feasible set in order for its projection to be a solution of the problem. Our analysis relies on a "sharpness" property of the constraint set; a new property we introduce here.

DOI: 10.48550/arXiv.2210.11252