Browder–Minty theorem

The Browder-Minty theorem is a fundamental result in the field of convex analysis and optimization, particularly related to the study of variational inequalities and monotone operators. It establishes the existence of solutions to certain types of variational inequalities under specific conditions. In its most general form, the theorem addresses the following setting: 1. **Hilbert Spaces**: Consider a Hilbert space \( H \).