Lipschitz continuity

Bài giảng "Tối ưu hóa nâng cao - Chương 7: Subgradient method" cung cấp cho người học các kiến thức: Last last time - gradient descent, subgradient method, step size choices, convergence analysis, lipschitz continuity, convergence analysis - Proof,... Mời các bạn cùng tham khảo.

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PERIODIC BOUNDARY VALUE PROBLEMS ON TIME SCALES ´ PETR STEHLIK Received 20 April 2004 We extend the results concerning periodic boundary value problems from the continuous calculus to time scales. First we use the Schauder fixed point theorem and the concept of lower and upper solutions to prove the existence of the solutions and then we investigate a monotone iterative method which could generate some of them. Since this method does not work on each time scale, a condition containing a Lipschitz constant of right-hand side function and the supremum of the graininess function is introduced.

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