Single-Projection Procedure for Infinite Dimensional Convex Optimization Problems
研究希尔伯特空间中一类可通过单次投影求解的凸优化问题，放宽了线性规划中严格互补条件等限制，并给出了不可行点与可行集所需距离的定量估计。
.We consider a class of convex optimization problems in a 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 complementarity conditions, and (iii) possess nonlinear 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.Keywordslinear programmingpolytopes and polyhedral setsconvex programmingHilbert spaceprojection methodsharpness propertysubtransversalityMSC codes90C0590C2549J5349J52