Radial Duality: turning constrained optimization into unconstrained Lipschitz problems
prof_grimmer · x · 2026-09-21
Alex Shtf recommends Benjamin Grimmer's paper 'Radial Duality Part I: Foundations' (arXiv:2104.11179). It generalizes Renegar's 2016 idea with radial transformations that convert arbitrary constrained/conic problems into equivalent unconstrained, uniformly Lipschitz minimization — no convex cones needed, enabling projection-free first-order methods even for nonconvex objectives. The transform is self-inverse for all concave objectives, yielding a new 'radial duality' plus a full calculus.
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