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Oleg Burdakov(oleg.burdakovliu.se) Abstract: 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 PoolAdjacentViolators (SPAV) algorithm is designed for solving the SMR. It belongs to the class of dual activeset algorithms. We proved its finite 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 largescale 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 $n$. Keywords: Monotonic regression, regularization, quadratic penalty, convex quadratic optimization, dual activeset method, largescale optimization. Category 1: Applications  Science and Engineering (Statistics ) Category 2: Nonlinear Optimization (Quadratic Programming ) Citation: Technical Report LiTHMATR2016/02SE, Department of Mathematics, Linkoping University, 2016 Download: [PDF] Entry Submitted: 06/30/2016 Modify/Update this entry  
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