- Accelerated gradient sliding for structured convex optimization Guanghui Lan(george.lanisye.gatech.edu) Yuyuan Ouyang(yuyuanoclemson.edu) Abstract: Our main goal in this paper is to show that one can skip gradient computations for gradient descent type methods applied to certain structured convex programming (CP) problems. To this end, we first present an accelerated gradient sliding (AGS) method for minimizing the summation of two smooth convex functions with different Lipschitz constants. We show that the AGS method can skip the gradient computation for one of these smooth components without slowing down the overall optimal rate of convergence. This result is much sharper than the classic black-box CP complexity results especially when the difference between the two Lipschitz constants associated with these components is large. We then consider an important class of bilinear saddle point problem whose objective function is given by the summation of a smooth component and a nonsmooth one with a bilinear saddle point structure. Using the aforementioned AGS method for smooth composite optimization and Nesterov's smoothing technique, we show that one only needs ${\cal O}(1/\sqrt{\epsilon})$ gradient computations for the smooth component while still preserving the optimal ${\cal O}(1/\epsilon)$ overall iteration complexity for solving these saddle point problems. We demonstrate that even more significant savings on gradient computations can be obtained for strongly convex smooth and bilinear saddle point problems. Keywords: convex programming, accelerated gradient sliding, structure, complexity, Nesterov’s method Category 1: Nonlinear Optimization Category 2: Convex and Nonsmooth Optimization Citation: Download: [PDF]Entry Submitted: 09/15/2016Entry Accepted: 09/15/2016Entry Last Modified: 09/15/2016Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.