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• W2570286083 abstract "We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration solves a regularized subproblem formed by linearizing the smooth map. When the subproblems are solved exactly, the method has efficiency $mathcal{O}(varepsilon^{-2})$, akin to gradient descent for smooth minimization. We show that when the subproblems can only be solved by first-order methods, a simple combination of smoothing, the prox-linear method, and a fast-gradient scheme yields an algorithm with complexity $widetilde{mathcal{O}}(varepsilon^{-3})$. The technique readily extends to minimizing an average of $m$ composite functions, with complexity $widetilde{mathcal{O}}(m/varepsilon^{2}+sqrt{m}/varepsilon^{3})$ in expectation. We round off the paper with an inertial prox-linear method that automatically accelerates in presence of convexity." @default.
• W2570286083 created "2017-01-13" @default.
• W2570286083 creator A5033142494 @default.
• W2570286083 creator A5073457791 @default.
• W2570286083 date "2016-04-30" @default.
• W2570286083 modified "2023-09-27" @default.
• W2570286083 title "Efficiency of minimizing compositions of convex functions and smooth maps" @default.
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• W2570286083 hasPublicationYear "2016" @default.
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