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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1999 • Question 4

Question

Math 6420 • PDE Fall 1999 • Question 4

Let \(C\) be a closed convex set in a Hilbert space \(H\), and let \(u\) be an arbitrary vector in \(H\). Show that there exists one and only one element in \(C\) which is closest to \(u\).

Raw LaTeX

Let \(C\) be a closed convex set in a Hilbert space \(H\), and let
\(u\) be an arbitrary vector in \(H\). Show that there exists one and only one element in \(C\)
which is closest to \(u\).

Topic Tags

Convex Sets and Projection Theorems Hilbert Spaces and Orthogonality Linear Programming and Optimization