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Convex Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems using Lyapunov functions

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Document pages: 15 pages

Abstract: This paper considers the problem of designing accelerated gradient-basedalgorithms for optimization and saddle-point problems. The class of objectivefunctions is defined by a generalized sector condition. This class of functionscontains strongly convex functions with Lipschitz gradients but also non-convexfunctions, which allows not only to address optimization problems but alsosaddle-point problems. The proposed design procedure relies on a suitable classof Lyapunov functions and on convex semi-definite programming. The proposedsynthesis allows the design of algorithms that reach the performance ofstate-of-the-art accelerated gradient methods and beyond.

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