Research map / Optimization / Nonconvex and smooth optimization
Solving Non-smooth Constrained Programs with Lower Complexity than $\mathcal{O}(1/\varepsilon)$: A Primal-Dual Homotopy Smoothing Approach
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use multi-stage homotopy smoothing under a local error bound | Linearly constrained convex programs · Linearly constrained convex programs with a local error bound | primal convergence time: O(1/\varepsilon) -> O\left(\varepsilon^{-2/(2+\beta)}\log_2(\varepsilon^{-1})\right) | Helped |
| Apply the method when the dual function is non-smooth but locally quadratic (β=1/2) | Primal-dual homotopy smoothing · Distributed geometric median | convergence time: \mathcal{O}\left(1/\varepsilon\right) -> \mathcal O\left(\varepsilon^{-4/5}\log_2(\varepsilon^{-1})\right) | Helped |
| Compare the proposed algorithm with existing algorithms in simulations | Distributed geometric median · Random networks with n=20, 50, 100 | relative error | Mixed |
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