Radial Duality paper turns constrained optimization into unconstrained Lipschitz problems
prof_grimmer · x · 2026-09-21
A recommended optimization paper, "Radial Duality Part I: Foundations" (arXiv:2104.11179) by Benjamin Grimmer:
- Transforms arbitrary constrained optimization problems into equivalent unconstrained ones with uniformly Lipschitz objectives, generalizing Renegar's 2016 approach.
- Radial transformations avoid reliance on convex cones/functions and work even with nonconvex objectives and constraint sets, enabling new projection-free first-order methods.
- The transform is self-inverse (dual) for a broad class of functions including all concave objectives, yielding a new duality; continuity, differentiability and convexity under the transform are characterized.
- Part II builds projection-free radial optimization algorithms on these foundations.
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