ЗАСЕДАНИЕ СЕМИНАРА «ПРОБЛЕМЫ ОПТИМИЗАЦИИ»

27 июля 2017 г. в 15:00 состоится очередное заседание семинара "Проблемы оптимизации" под руководством академика РАН Ю.Г. Евтушенко.

Место проведения мероприятия: ВЦ РАН Центра (ул. Вавилова, 40, 3-й этаж, кабинет № 322)

На семинаре будет представлен доклад по теме

"A DUAL ACTIVE-SET ALGORITHM FOR REGULARIZED MONOTONIC REGRESSION"

Докладчик – профессор Олег Бурдаков,  Linkoping University (Швеция)

Аннотация доклада

Monotonic (isotonic) Regression (MR) is a powerful tool used for solving a wide range of important applied problems. One of its features, which poses a limitation on its use in some areas, is that it produces a piecewise constant fitted response. For smoothing the fitted response, we introduce a regularization term in the MR formulated as a least distance problem with monotonicity constraints. The resulting Smoothed Monotonic Regrassion (SMR) is a convex quadratic optimization problem. We focus on the SMR, where the set of observations is completely (linearly) ordered. Our Smoothed Pool-Adjacent-Violators (SPAV) algorithm is designed for solving the SMR. It belongs to the class of dual active-set algorithms. We proved its nite convergence to the optimal solution in, at most, n iterations, where n is the problem size. One of its advantages is that the active set is progressively enlarging by including one or, typically, more constraints per iteration. This resulted in solving large-scale SMR test problems in a few iterations, whereas the size of that problems was prohibitively too large for the conventional quadratic optimization solvers. Although the complexity of the SPAV algorithm is O(n^2), its running time was growing in our computational experiments almost linearly with n.

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