[Home ] [Archive]    
:: Main :: About :: Current Issue :: Archive :: Search :: Submit :: Registration ::
:: Volume 8, Issue 2 (5-2017) ::
IJOR 2017, 8(2): 40-47 Back to browse issues page
A Dual Active-Set Algorithm for Regularized Slope-Constrained Monotonic Regression
Oleg Burdakov , Oleg Sysoev
Linkӧping University , oleg.burdakov@liu.se
Abstract:   (5224 Views)
In many problems, it is necessary to take into account monotonic relations. Monotonic (isotonic) Regression (MR) is often involved in solving such problems. The MR solutions are of a step-shaped form with a typical sharp change of values between adjacent steps. This, in some applications, is regarded as a disadvantage. We recently introduced a Smoothed MR (SMR) problem which is obtained from the MR by adding a regularization penalty term. The SMR is aimed at smoothing the aforementioned sharp change. Moreover, its solution has a far less pronounced step-structure, if at all available. The purpose of this paper is to further improve the SMR solution by getting rid of such a structure. This is achieved by introducing a lowed bound on the slope in the SMR. We call it Smoothed Slope-Constrained MR (SSCMR) problem. It is shown here how to reduce it to the SMR which is a convex quadratic optimization problem. The Smoothed Pool Adjacent Violators (SPAV) algorithm developed in our recent publications for solving the SMR problem is adapted here to solving the SSCMR problem. This algorithm belongs to the class of dual active-set algorithms. Although the complexity of the SPAV algorithm is $𝑂(𝑛^2)$, its running time is growing in our computational experiments almost linearly with $𝑛$. We present numerical results which illustrate the predictive performance quality of our approach. They also show that the SSCMR solution is free of the undesirable features of the MR and SMR solutions.
Keywords: Monotonic regression, Regularization, Quadratic penalty, Convex quadratic optimization, Dual active-set method, Large-scale optimization.
Full-Text [PDF 545 kb]   (4821 Downloads)    
Type of Study: Original | Subject: Other
Received: 2018/05/28 | Accepted: 2018/05/28 | Published: 2018/05/28
Send email to the article author

Add your comments about this article
Your username or Email:


XML     Print

Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Volume 8, Issue 2 (5-2017) Back to browse issues page
مجله انجمن ایرانی تحقیق در عملیات Iranian Journal of Operations Research
Persian site map - English site map - Created in 0.06 seconds with 30 queries by YEKTAWEB 4343