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Generalized shape constrained spline fitting for qualitative analysis of trends

COMPUTERS & CHEMICAL ENGINEERING 2013年 58卷 116-134页

作者： Villez, Kris Venkatasubramanian, Venkat Rengaswamy, Raghunathan Purdue Univ Sch Chem Engn Lab Intelligent Proc Syst W Lafayette IN 47907 USA Columbia Univ Dept Chem Engn New York NY 10027 USA Indian Inst Technol Madras Dept Chem Engn Madras Tamil Nadu India

In this work, we present a generalized method for analysis of data series based on shape constraint spline fitting which constitutes the first step toward a statistically optimal method for qualitative analysis of trends. The presented method is based on a branch-and-bound (B&B) algorithm which is applied for globally optimal fitting of a spline function subject to shape constraints. More specifically, the B&B algorithm searches for optimal argument values in which the sign of the fitted function and/or one or more of its derivatives change. We derive upper and lower bounding procedures for the B& B algorithm to efficiently converge to the global optimum. These bounds are based on existing solutions for shape constraint spline estimation via second order cone Programs (SOCPs). The presented method is demonstrated with three different examples which are indicative of both the strengths and weaknesses of this method. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Data mining Fault diagnosis Qualitative trend analysis Spline functions Global optimization second order cone programming

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On p-norm linear discrimination

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第3期231卷 784-789页

作者： Morenko, Yana Vinel, Alexander Yu, Zhaohan Krokhmal, Pavlo Univ Iowa Dept Mech & Ind Engn Iowa City IA 52242 USA

We consider a p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to a linear programming problem with p-order cone constraints. The proposed approach for handling linear programming problems with p-order cone constraints is based on reformulation of p-order cone optimization problems as second order cone programming (SOCP) problems when p is rational. Since such reformulations typically lead to SOCP problems with large numbers of second order cones, an "economical" representation that minimizes the number of second order cones is proposed. A case study illustrating the developed model on several popular data sets is conducted. (c) 2013 Elsevier B.V. All rights reserved.

关键词： Linear separation p-order cone programming second order cone programming

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Approximate Least Trimmed Sum of Squares Fitting and Applications in Image Analysis

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2013年第5期22卷 1836-1847页

作者： Shen, Fumin Shen, Chunhua van den Hengel, Anton Tang, Zhenmin Nanjing Univ Sci & Technol Sch Comp Sci & Technol Nanjing 210094 Jiangsu Peoples R China Univ Adelaide Australian Ctr Visual Technol Canberra ACT 5005 Australia Univ Adelaide Sch Comp Sci Canberra ACT 5005 Australia

The least trimmed sum of squares (LTS) regression estimation criterion is a robust statistical method for model fitting in the presence of outliers. Compared with the classical least squares estimator, which uses the entire data set for regression and is consequently sensitive to outliers, LTS identifies the outliers and fits to the remaining data points for improved accuracy. Exactly solving an LTS problem is NP-hard, but as we show here, LTS can be formulated as a concave minimization problem. Since it is usually tractable to globally solve a convex minimization or concave maximization problem in polynomial time, inspired by [1], we instead solve LTS' approximate complementary problem, which is convex minimization. We show that this complementary problem can be efficiently solved as a second order cone program. We thus propose an iterative procedure to approximately solve the original LTS problem. Our extensive experiments demonstrate that the proposed method is robust, efficient and scalable in dealing with problems where data are contaminated with outliers. We show several applications of our method in image analysis.

关键词： Least trimmed sum of squares (LTS) regression outlier removal robust model fitting second order cone programming semidefinite programming

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Robust twin support vector machine for pattern classification

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PATTERN RECOGNITION 2013年第1期46卷 305-316页

作者： Qi, Zhiquan Tian, Yingjie Shi, Yong Chinese Acad Sci Res Ctr Fictitious Econ & Data Sci Beijing 100190 Peoples R China

In this paper, we proposed a new robust twin support vector machine (called R-TWSVM) via second order cone programming formulations for classification, which can deal with data with measurement noise efficiently. Preliminary experiments confirm the robustness of the proposed method and its superiority to the traditional robust SVM in both computation time and classification accuracy. Remarkably, since there are only inner products about inputs in our dual problems, this makes us apply kernel trick directly for nonlinear cases. Simultaneously we does not need to solve the extra inverse of matrices, which is totally different with existing TWSVMs. In addition, we also show that the TWSVMs are the special case of our robust model and simultaneously give a new dual form of TWSVM by degenerating R-TWSVM, which successfully overcomes the existing shortcomings of TWSVM. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Classification Twin support vector machine second order cone programming Robust

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A locking-free stabilized kinematic EFG model for plane strain limit analysis

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COMPUTERS & STRUCTURES 2012年第Sep.期106卷 1-8页

作者： Le, C. V. Askes, H. Gilbert, M. Univ Sheffield Dept Civil & Struct Engn Sheffield S10 2TN S Yorkshire England Int Univ VNU HCMC Dept Civil Engn Ho Chi Minh City Vietnam

An element free Galerkin (EFG) based formulation for limit analysis of rigid-perfectly plastic plane strain problems is presented. In the paper it is demonstrated that volumetric locking and instability problems can be avoided by using a stabilized conforming nodal integration scheme. Furthermore, the stabilized EFG method described allows stable and accurate solutions to be obtained with minimal computational effort. The discrete kinematic formulation is cast in the form of a second-order cone problem, allowing efficient interior-point solvers to be used to obtain solutions. Finally, the performance of the stabilized EFG method is illustrated by considering several numerical examples. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Limit analysis Meshless methods Volumetric locking Strain smoothing Nodal integration second order cone programming

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Variable selection of varying coefficient models in quantile regression

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ELECTRONIC JOURNAL OF STATISTICS 2012年第none期6卷 1220-1238页

作者： Noh, Hohsuk Chung, Kwanghun Van Keilegom, Ingrid Catholic Univ Louvain Inst Stat Biostat & Sci Actuarielles B-1348 Louvain Belgium Hongik Univ Coll Business Adm Seoul 121791 South Korea

Varying coefficient (VC) models are commonly used to study dynamic patterns in many scientific areas. In particular, VC models in quantile regression are known to provide a more complete description of the response distribution than in mean regression. In this paper, we develop a variable selection method for VC models in quantile regression using a shrinkage idea. The proposed method is based on the basis expansion of each varying coefficient and the regularization penalty on the Euclidean norm of the corresponding coefficient vector. We show that our estimator is obtained as an optimal solution to the second order cone programming (SOCP) problem and that the proposed procedure has consistency in variable selection under suitable conditions. Further, we show that the estimated relevant coefficients converge to the true functions at the univariate optimal rate. Finally, the method is illustrated with numerical simulations including the analysis of forced expiratory volume (FEV) data.

关键词： Basis approximation consistency in variable selection second order cone programming shrinkage estimator

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Berth allocation considering fuel consumption and vessel emissions

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2011年第6期47卷 1021-1037页

作者： Du, Yuquan Chen, Qiushuang Quan, Xiongwen Long, Lei Fung, Richard Y. K. Nankai Univ Ctr Logist Technol Tianjin 300071 Peoples R China Tianjin Port & Shipping Dev Res Ctr Tianjin 300461 Peoples R China City Univ Hong Kong Dept Mfg Engn & Engn Management Hong Kong Hong Kong Peoples R China

We propose a more elaborate model on berth allocation considering fuel consumption than before, and overcome the nonlinear complexity by casting it as a mixed integer second order cone programming model. Furthermore, we conduct the vessel emission (in sailing periods) calculation with the widely-used emission factors. Besides, vessel emissions in mooring periods are also analyzed through a post-optimization phase on waiting time. Experimental results demonstrate that the new berth allocation strategy, reflected by the proposed model, is competent to significantly reduce fuel consumption and vessel emissions, while simultaneously retaining the service level of the terminal. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Berth allocation Fuel consumption Emission second order cone programming Port-shipping coordination

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Design of Radar Receive Filters Optimized According to L_p-Norm Based Criteria

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2011年第8期59卷 4023-4029页

作者： De Maio, Antonio Huang, Yongwei Piezzo, Marco Zhang, Shuzhong Farina, Alfonso Univ Naples Federico 2 Dipartimento Ingn Biomed Elettron & Telecomunicaz I-80125 Naples Italy Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China Univ Minnesota Program Ind & Syst Engn Minneapolis MN 55455 USA SELEX Sistemi Integrati I-00131 Rome Italy

This correspondence deals with the design of radar receive filters for pulse compression which optimize either the L-p-norm of the vector containing the filter sidelobe energies or the inverse signal-to-noise power ratio (ISNR) under an upper-bound constraint on the previously mentioned L-p-norm. In both the cases, we prove that the filter design can be formulated as a convex optimization second-order cone programming (SOCP) problem which can be efficiently solved with a polynomial time computational complexity resorting to interior point methods. At the analysis stage, we assess the performance of the receive filters in correspondence of different values of the parameter highlighting the performance compromises between the integrated sidelobe level (ISL), the peak sidelobe level (PSL), and the ISNR. Finally, we study the effects of the filter length on the performance as well as the Doppler tolerance of the devised filters. The results show that the proposed technique leads to satisfactory performance levels and good Doppler tolerances.

关键词： Mismatched filter design radar receive filter design second order cone programming

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Model predictive control with robust feasibility

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JOURNAL OF PROCESS CONTROL 2011年第3期21卷 415-435页

作者： Li, Xiang Marlin, Thomas E. McMaster Univ Dept Chem Engn Hamilton ON L8S 4L7 Canada

This paper presents a new model predictive control (MPC) method that provides robust feasibility with tractable, real-time computation. The method optimizes the closed-loop system dynamics, which involves models of the process (with parametric uncertainty) and controller at each step in the prediction horizon. Such problems are often formulated as a multi-stage stochastic program that suffers from the curse of dimensionality. This paper presents an alternative formulation that yields a bilevel stochastic optimization problem that is transformed by a series of reformulation steps into a tractable problem such that it can be solved through a limited number of second order cone programming sub-problems. The method addresses robust feasibility, manipulated saturation, state and output soft constraints, exogenous and endogenous uncertainty, and uncertainty in the state estimation in an integrated manner. Case study results demonstrate the advantages of the proposed robust MPC over nominal MPC and several other robust MPC formulations. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Model predictive control Robust MPC Robust feasibility Stochastic programming Bilevel optimization second order cone programming

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Solving second order cone programming via a reduced augmented system approach

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SIAM JOURNAL ON OPTIMIZATION 2006年第3期17卷 711-737页

作者： Cai, Zhi Toh, Kim-Chuan Singapore MIT Alliance HPCES Singapore 117576 Singapore Natl Univ Singapore Dept Math Singapore 117543 Singapore

The standard Schur complement equation-based implementation of interior-point methods for second order cone programming may encounter stability problems in the computation of search directions, and as a consequence, accurate approximate optimal solutions are sometimes not attainable. Based on the eigenvalue decomposition of the (1, 1) block of the augmented equation, a reduced augmented equation approach is proposed to ameliorate the stability problems. Numerical experiments show that the new approach can achieve more accurate approximate optimal solutions than the Schur complement equation-based approach.

关键词： second order cone programming augmented equation Nesterov-Todd direction stability

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