https://www.dualspace.blog/ A blog about optimization and mathematics — the dual of primalspace.me. https://www.dualspace.blog/blog/derivative-notation-1-problems/ https://www.dualspace.blog/blog/derivative-notation-1-problems/ Tue, 23 Dec 2025 12:00:00 GMT A collection of problems with standard derivative notation, from ambiguous variable references to inconsistent layout conventions. https://www.dualspace.blog/blog/mathematical-phenomena/ https://www.dualspace.blog/blog/mathematical-phenomena/ Mon, 24 Nov 2025 12:00:00 GMT Some personal observations about the phenomenology of doing mathematics. https://www.dualspace.blog/blog/generalizing-slater-condition/ https://www.dualspace.blog/blog/generalizing-slater-condition/ Thu, 30 Oct 2025 12:00:00 GMT We explore how Slater's constraint qualification for strong duality can be generalized from its classical form to settings where the spaces involved are generic vector spaces, even those lacking topological structure. https://www.dualspace.blog/blog/proximity-operator-matrix-norm/ https://www.dualspace.blog/blog/proximity-operator-matrix-norm/ Wed, 15 Oct 2025 12:00:00 GMT A closed-form expression for the proximity operator of x↦λ∥Mx∥2​, where M is any real-valued matrix.