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• W2794824917 abstract "In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a sufficient condition for exponential convergence of the algorithm. The entries of this matrix are polynomial functions of the unknown parameters (exponential decay rate, stepsize, momentum coefficient, etc.). We then formulate a polynomial optimization, in which the objective is to optimize the exponential decay rate over the parameters of the algorithm. Finally, we use sum-of-squares programming as a tractable relaxation of the proposed polynomial optimization problem. We illustrate the utility of the proposed framework by designing a first-order algorithm that shares the same structure as Nesterov's accelerated gradient method." @default.
• W2794824917 created "2018-04-06" @default.
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• W2794824917 creator A5043154223 @default.
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• W2794824917 date "2018-03-29" @default.
• W2794824917 modified "2023-09-24" @default.
• W2794824917 title "Design of First-Order Optimization Algorithms via Sum-of-Squares Programming" @default.
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• W2794824917 hasPublicationYear "2018" @default.
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