An inexact augmented Lagrangian multiplier method for solving quadratic complementary problems: An adapted algorithmic framework combining specific resolution techniques

Hu, Shenglong; Wang, Jie; Huang, Zheng-Hai

doi:10.1016/j.cam.2019.04.020

Cited by 13 publications

(4 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The constrained minimization problem can be solved by an augmented Lagrangian multiplier (ALM) method (Hu et al, 2019 ); see Supplementary Material . The ALM function for Equation (7) is…”

Section: Methodsmentioning

confidence: 99%

A Novel Early-Stage Lung Adenocarcinoma Prognostic Model Based on Feature Selection With Orthogonal Regression

Tang

Wang

Chen

et al. 2021

Front. Cell Dev. Biol.

View full text Add to dashboard Cite

Carcinoma diagnosis and prognosis are still hindered by the lack of effective prediction model and integration methodology. We proposed a novel feature selection with orthogonal regression (FSOR) method to resolve predictor selection and performance optimization. Functional enrichment and clinical outcome analyses with multi-omics information validated the method's robustness in the early-stage prognosis of lung adenocarcinoma. Furthermore, compared with the classic least absolute shrinkage and selection operator (LASSO) regression method [the averaged 1- to 4-years predictive area under the receiver operating characteristic curve (AUC) measure, 0.6998], the proposed one outperforms more accurately by 0.7208 with fewer predictors, particularly its averaged 1- to 3-years AUC reaches 0.723, vs. classic 0.6917 on The Cancer Genome Atlas (TCGA). In sum, the proposed method can deliver better prediction performance for early-stage prognosis and improve therapy strategy but with less predictor consideration and computation burden. The self-composed running scripts, together with the processed results, are available at https://github.com/gladex/PM-FSOR.

show abstract

“…The constrained minimization problem can be solved by an augmented Lagrangian multiplier (ALM) method (Hu et al, 2019 ); see Supplementary Material . The ALM function for Equation (7) is…”

Section: Methodsmentioning

confidence: 99%

A Novel Early-Stage Lung Adenocarcinoma Prognostic Model Based on Feature Selection With Orthogonal Regression

Tang

Wang

Chen

et al. 2021

Front. Cell Dev. Biol.

View full text Add to dashboard Cite

show abstract

“…where a is any n-dimensional vector, and a large J indicates a large ratio between different categories and similar categories, and suggests a strong linear separability among different categories. Letting a T S W a = 1, according to the Lagrangian multiplier method [32], equation ( 6) is equivalent to the following:…”

Section: Lda Algorithmmentioning

confidence: 99%

Feature extraction method of rolling bearing based on adaptive divergence matrix linear discriminant analysis

Shi

Cao

Liu

et al. 2021

Meas. Sci. Technol.

View full text Add to dashboard Cite

Status feature extraction is crucial to bearing fault diagnosis and the maintenance of rotating machinery. There are many challenges in extracting the effective status features from vibration signals for bearing fault diagnosis. A linear discriminant analysis (LDA) based on an adaptive divergence matrix (ALDA) is proposed to extract the status features of rolling bearings in this paper. The main idea of the method is that the sample clustering evaluation index (SI) is used to adjust the weight of the within-class divergence matrix of the LDA algorithm to reduce the cross or overlap among different types of samples, especially for the marginal samples. In the method, vibration signals of the rolling bearing under different running conditions are acquired, and the original features, such as time domain and frequency domain, are extracted from the vibration signals. Then, the optimal exponential weight of the within-class divergence matrix of the LDA is selected with the maximum SI. The optimal fusion status features of the bearing under different conditions were extracted by the ALDA algorithm from the original features. Finally, the fusion features were identified by the support vector machine classifier to verify the effectiveness of the proposed method. The experimental results show that the bearing status features extracted by ALDA can be used to identify the bearing status effectively.

show abstract

“…We have reviewed the developments of solution methods for TCPs. During the evaluation of this paper, we find two new algorithms for TCPs were proposed: Hu et al [62] proposed an inexact augmented Lagrangian multiplier method for solving quadratic complementary problems, and Chen and Zhang [63] proposed a semismooth Newton method to find a Nash equilibrium for the multi-person noncooperative game via solving the corresponding TCP.…”

Section: Perspectives and Open Problemsmentioning

confidence: 99%

Tensor Complementarity Problems—Part II: Solution Methods

Huang

2019

J Optim Theory Appl

Self Cite

View full text Add to dashboard Cite

This work, with its three parts, reviews the state-of-the-art of studies for the tensor complementarity problem and some related models. In the first part of this paper, we have reviewed the theoretical developments of the tensor complementarity problem and related models. In this second part, we review the developments of solution methods for the tensor complementarity problem. It has been shown that the tensor complementarity problem is equivalent to some known optimization problems, or related problems such as systems of tensor equations, systems of nonlinear equations, and nonlinear programming problems, under suitable assumptions. By solving these reformulated problems with the help of structures of the involved tensors, several numerical methods have been proposed so that a solution of the tensor complementarity problem can be found. Moreover, based on a polynomial optimization model, a semidefinite relaxation method is presented so that all solutions of the tensor complementarity problem can be found under the assumption that the solution set of the problem is finite. Further applications of the tensor complementarity problem will be given and discussed in the third part of this paper. KeywordsTensor complementarity problem • System of tensor equations • System of non-smooth equations • Mixed integer programming • Semidefinite relaxation method Mathematics Subject Classification 90C33 • 90C30 • 65H10 B Liqun Qi

show abstract

An inexact augmented Lagrangian multiplier method for solving quadratic complementary problems: An adapted algorithmic framework combining specific resolution techniques

Cited by 13 publications

References 14 publications

A Novel Early-Stage Lung Adenocarcinoma Prognostic Model Based on Feature Selection With Orthogonal Regression

A Novel Early-Stage Lung Adenocarcinoma Prognostic Model Based on Feature Selection With Orthogonal Regression

Feature extraction method of rolling bearing based on adaptive divergence matrix linear discriminant analysis

Tensor Complementarity Problems—Part II: Solution Methods

Contact Info

Product

Resources

About