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Adaptive Smoothing Algorithms for Nonsmooth Composite Convex Minimization | | Quoc Tran-Dinh
; | | Date: |
1 Sep 2015 | | Abstract: | We propose a novel adaptive smoothing algorithm based on Nesterov’s smoothing
technique in cite{Nesterov2005c} for solving nonsmooth composite convex
optimization problems. Our method combines both Nesterov’s accelerated proximal
gradient scheme and a new homotopy strategy for smoothness parameter. By an
appropriate choice of smoothing functions, we develop a new algorithm that has
the $mathcal{O}left(frac{1}{varepsilon}
ight)$ optimal worst-case
iteration-complexity while allows one to automatically update the smoothness
parameter at each iteration. We then further exploit the structure of problems
to select smoothing functions and develop suitable algorithmic variants that
reduce the complexity-per-iteration, while preserve the optimal worst-case
iteration-complexity. We also specify our algorithm to solve constrained convex
optimization problems and show its convergence guarantee on the primal sequence
of iterates. Our preliminarily numerical tests verify the efficiency of our
algorithms. | | Source: | arXiv, 1509.0106 | | Services: | Forum | Review | PDF | Favorites | |
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