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arXiv · 2210.11252

Single-Projection Procedure for Infinite Dimensional Convex Optimization Problems

Hoa T. Bui·Regina S. Burachik·Evgeni A. Nurminski·Matthew K. Tam
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Abstract

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: (i) may have multiple solutions, (ii) do not satisfy strict complementary conditions, and (iii) 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.

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Hoa T. Bui, Regina S. Burachik, Evgeni A. Nurminski, Matthew K. Tam. 2022-10-20. Single-Projection Procedure for Infinite Dimensional Convex Optimization Problems. https://arxiv.org/abs/2210.11252

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