In this paper, we propose a robust blind multiuser detector for code-division multiple access (CDMA) systems against signature waveform mismatch (SWM) derived from the influences of time asynchronization or channel di...
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In this paper, we propose a robust blind multiuser detector for code-division multiple access (CDMA) systems against signature waveform mismatch (SWM) derived from the influences of time asynchronization or channel distortion. This blind detection method with SWM problem is formulated as blind source separation (BSS) model subject to the second-ordercone (SOC) constraint. The resulting blind separation based on SOC programming problem is solved by approximate negentropy maximization using quasi-Newton iterative methods. Theoretical analysis and simulation results show that the performance of the proposed blind detector is superior to those of the existing methods.
In order to improve the robustness of the noise source identification and localization in high SNR environment, a new minimum variance distortion response algorithm (AC-SOCP-MVDR) is proposed in this paper. The propos...
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In order to improve the robustness of the noise source identification and localization in high SNR environment, a new minimum variance distortion response algorithm (AC-SOCP-MVDR) is proposed in this paper. The proposed method combines secondorderconeprogramming (SOCP) with near-field amplitude compensation (AC). On the basis of previous MVDR focused beam-former, this new method imposes the inequality norm constraint on the steering vector, and then it acquires the optional steering vector by YALMIP toolbox and amplitude compensation. It can improve the robustness of beam-former and achieve the true source level of noise in near-field. Simulation and experimental studies prove that AC-SOCP-MVDR is a practical and feasible method, which can realize identification and localization of noise source, not only estimate the relative value but also the true signal of interest (SOI) power in high SNR environment.
This study concerns a method of selecting the best subset of explanatory variables in a multiple linear regression model. Goodness-of-fit measures, for example, adjusted R-2, AIC, and BIC, are generally used to evalua...
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This study concerns a method of selecting the best subset of explanatory variables in a multiple linear regression model. Goodness-of-fit measures, for example, adjusted R-2, AIC, and BIC, are generally used to evaluate a subset regression model. Although variable selection with regard to these measures is usually performed with a stepwise regression method, it does not always provide the best subset of explanatory variables. In this paper, we propose mixed integer second-order cone programming formulations for selecting the best subset of variables with respect to adjusted R-2, AIC, and BIC. Computational experiments show that, in terms of these measures, the proposed formulations yield better solutions than those provided by common stepwise regression methods. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
This work addresses the issue of high dimensionality for linear multiclass Support Vector Machines (SVMs) using second-order cone programming (SOCP) formulations. These formulations provide a robust and efficient fram...
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This work addresses the issue of high dimensionality for linear multiclass Support Vector Machines (SVMs) using second-order cone programming (SOCP) formulations. These formulations provide a robust and efficient framework for classification, while an adequate feature selection process may improve predictive performance. We extend the ideas of SOCP-SVM from binary to multiclass classification, while a sequential backward elimination algorithm is proposed for variable selection, defining a contribution measure to determine the feature relevance. Experimental results with multiclass microarray datasets demonstrate the effectiveness of a low-dimensional data representation in terms of performance.
This paper presents an exact penalty method for solving optimization problems with very general constraints covering, in particular, nonlinear programming (NLP), semidefinite programming (SDP), and second-ordercone p...
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This paper presents an exact penalty method for solving optimization problems with very general constraints covering, in particular, nonlinear programming (NLP), semidefinite programming (SDP), and second-order cone programming (SOCP). The algorithm is called the sequential linear cone method (SLCM) because for SDP and SOCP the main cost of computation amounts to solving at each iteration a linear cone program for which efficient solvers are available. Restricted to NLP, SLCM is exactly a sequential quadratic program method. Under two basic conditions which concern only the data, it is proved that the sequence of iterates is bounded. Furthermore, in particular, when the feasible set is nonempty, under two additional constraint qualification conditions, it is proved that the cluster points are stationary points. In that case, it is established also that the sequence of penalty parameters eventually stays constant, and for a particular class of data it is proved that a unit step length can be obtained.
The smoothing-type algorithm is a powerful tool for solving the second-order cone programming (SOCP), which is in general designed based on a monotone line search. In this paper, we propose a smoothing-type algorithm ...
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The smoothing-type algorithm is a powerful tool for solving the second-order cone programming (SOCP), which is in general designed based on a monotone line search. In this paper, we propose a smoothing-type algorithm for solving the SOCP with a non-monotone line search. By using the theory of Euclidean Jordan algebras, we prove that the proposed algorithm is globally and locally quadratically convergent under suitable assumptions. The preliminary numerical results are also reported which indicate that the non-monotone smoothing-type algorithm is promising for solving the SOCP.
This work addresses the numerical computation of the two-dimensional flow of yield stress fluids (with Bingham and Herschel-Bulkley models) based on a variational approach and a finite element discretization. The main...
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This work addresses the numerical computation of the two-dimensional flow of yield stress fluids (with Bingham and Herschel-Bulkley models) based on a variational approach and a finite element discretization. The main goal of this paper is to propose an alternative optimization method to existing procedures such as penalization and augmented Lagrangian techniques. It is shown that the minimum principle for Bingham and Herschel-Bulkley yield stress fluid steady flows can, indeed, be formulated as a second-order cone programming (SOCP) problem, for which very efficient primal-dual interior point solvers are available. In particular, the formulation does not require any regularization of the visco-plastic model as is usually the case for existing techniques, avoiding therefore the difficult choice of the regularization parameter. Besides, it is also unnecessary to adopt a mixed stress-velocity approach or discretize explicitly auxiliary variables as frequently proposed in existing methods. Finally, the performance of dedicated SOCP solvers, like the MOSEK software package, enables us to solve large-scale problems on a personal computer within seconds only. The proposed method will be validated on classical benchmark examples and used to simulate the flow generated around a plate during its withdrawal from a bath of yield stress fluid. (C) 2014 Elsevier B.V. All rights reserved.
Feature selection is an important machine learning topic, especially in high dimensional applications, such as cancer prediction with microarray data. This work addresses the issue of high dimensionality of feature se...
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Feature selection is an important machine learning topic, especially in high dimensional applications, such as cancer prediction with microarray data. This work addresses the issue of high dimensionality of feature selection for linear and kernel-based Support Vector Machines (SVMs) considering second-order cone programming formulations. These formulations provide a robust and efficient framework for classification, while an adequate feature selection process avoids errors in the estimation of means and covariances. Our approach is based on a sequential backward elimination which uses different linear and kernel-based contribution measures to determine the feature relevance. Experimental results with microarray datasets demonstrate the effectiveness in terms of predictive performance and construction of a low-dimensional data representation.
The maximum-crossrange problem is an optimal control problem of computing the maximum crossrange reachable by a hypersonic entry vehicle at a specified downrange, which has long known to be very difficult to solve due...
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The maximum-crossrange problem is an optimal control problem of computing the maximum crossrange reachable by a hypersonic entry vehicle at a specified downrange, which has long known to be very difficult to solve due to its high nonlinearities and non-convexity. This paper presents how to convexify the problem so that it can be efficiently solved by successive second-order cone programming (SOCP). Particular focus is given on equivalent transformation of the original optimization objective and rigorous establishment of validity of the relaxation process used for convexification. In addition, it is observed that iteratively solving the SOCP problems may not always guarantee convergence to the original problem, a simple line search approach is proposed which is found critical to ensure the convergence of the successive SOCP method. Numerical demonstrations are provided to illustrate the effectiveness and efficiency of the proposed method and its applicability to both orbital and suborbital missions. (C) 2015 Elsevier Masson SAS. All rights reserved.
Let the design of an experiment be represented by an s-dimensional vector w of weights with nonnegative components. Let the quality of w for the estimation of the parameters of the statistical model be measured by the...
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Let the design of an experiment be represented by an s-dimensional vector w of weights with nonnegative components. Let the quality of w for the estimation of the parameters of the statistical model be measured by the criterion of D-optimality, defined as the mth root of the determinant of the information matrix M(w) = Sigma(s)(i=1) w(i)A(i)A(i)(T), where A(i), i = 1, ... , s are known matrices with in rows. In this paper, we show that the criterion of D-optimality is second-ordercone representable. As a result, the method of second-order cone programming can be used to compute an approximate D-optimal design with any system of linear constraints on the vector of weights. More importantly, the proposed characterization allows us to compute an exact D-optimal design, which is possible thanks to high-quality branch-and-cut solvers specialized to solve mixed integer second-order cone programming problems. Our results extend to the case of the criterion of D-K-optimality, which measures the quality of w for the estimation of a linear parameter subsystem defined by a full-rank coefficient matrix K. We prove that some other widely used criteria are also second-ordercone representable, for instance, the criteria of A-, A(K)-, G- and I-optimality. We present several numerical examples demonstrating the efficiency and general applicability of the proposed method. We show that in many cases the mixed integer second-order cone programming approach allows us to find a provably optimal exact design, while the standard heuristics systematically miss the optimum.
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