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A novel improved edge-based smoothed particle finite element method for elastoplastic contact analysis using second order cone programming

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2025年 441卷

作者： Zhou, Xi-Wen Jin, Yin-Fu Yin, Zhen-Yu Liu, Feng-Tao Chen, Xiangsheng Shenzhen Univ State Key Lab Intelligent Geotech & Tunnelling Shenzhen 518060 Guangdong Peoples R China Shenzhen Univ Natl Engn Res Ctr Deep Shaft Construct Shenzhen 518060 Guangdong Peoples R China Shenzhen Univ Coll Civil & Transportat Engn Shenzhen 518060 Guangdong Peoples R China Hong Kong Polytech Univ Dept Civil & Environm Engn Hung Hom Kowloon Hong Kong Peoples R China Guilin Univ Technol Guangxi Key Lab Geotech Mech Engn Guilin 541004 Peoples R China

Contact problems are of paramount importance in engineering but present significant challenges for numerical solutions due to their highly nonlinear nature. Recognizing that contact problems can be formulated as optimization problems with inequality constraints has paved the way for advanced techniques such as the Interior Point (IP) method. This study presents an Improved Edge-based Smoothed Particle Finite Element Method (IES-PFEM) with novel contact scheme for elastoplastic analysis involving large deformation using second-order cone programming (SOCP). Within the proposed framework, classical node-to-surface (NTS) and surface-to-surface (STS) contact discretization schemes in SOCP form are rigorously achieved. The governing equations of elastoplastic boundary value problems are formulated as a min-max problem via the mixed variation principle, and by applying the primal-dual theory of convex optimization, the problem is transformed into a dual formulation with stresses as optimization variables. The Mohr-Coulomb plastic yield criterion and the Coulomb friction law are naturally expressed as second-order cone constraints. A fixed-point iteration scheme is developed to address unphysical normal expansion arising from the natural derivation of an associated friction model within the SOCP formulation. Furthermore, the volumetric locking problem in nearly incompressible materials is alleviated by IES-PFEM formulation without requiring additional stabilization techniques. The proposed method is validated through a series of benchmark examples involving contact and elastoplastic deformations. Numerical results confirm the capability of the proposed approach to handle both contact and elastoplastic nonlinearities effectively, without the need for convergence control, highlighting the superiority of the proposed method.

关键词： second order cone programming Interior point method Contact Elastoplastic deformations Smoothed finite element method

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FSOCP: feature selection via second-order cone programming

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CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2025年第1期33卷 51-64页

作者： Guldogus, Buse Cisil Ozogur-Akyuz, Suereyya Bahcesehir Univ Dept Ind Engn Istanbul Turkiye Bahcesehir Univ Dept Math Istanbul Turkiye

Feature selection is an important factor of accurately classifying high dimensional data sets by identifying relevant features and improving classification accuracy. The use of feature selection in operations research allows for the identification of relevant features and the creation of optimal subsets of features for improved predictive performance. This paper proposes a novel feature selection algorithm inspired from ensemble pruning which involves the use of second-order conic programming modeled as an embedded feature selection technique with neural networks, named feature selection via second order cone programming (FSOCP). The proposed FSOCP algorithm trains features individually on a neural network and generates a probability class distribution and prediction, allowing the second-order conic programming model to determine the most important features for improved classification accuracies. The algorithm is evaluated on multiple synthetic data sets and compared with other feature selection techniques, demonstrating its promising potential as a feature selection approach.

关键词： Feature selection Feature extraction Neural networks Ensemble pruning second order cone programming

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second order cone programming approach to two-stage network data envelopment analysis

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第1期262卷 231-238页

作者： Chen, Kun Zhu, Joe Nanjing Audit Univ Coll Auditing & Evaluat Nanjing 211815 Jiangsu Peoples R China Worcester Polytech Inst Foisie Business Sch Worcester MA 01609 USA

Efficiency aggregation and efficiency decomposition are two techniques used in modeling decision making units (DMUs) with two-stage network structures under network data envelopment analysis (DEA). Multiplicative efficiency decomposition (MED) is usually used in a very specialized two-stage structure when constant returns to scale (CRS) is assumed. MED-based network DEA retains the property of the conventional DEA in the sense that input- and output-oriented models yield the same efficiency scores. Compared with the additive efficiency decomposition (AED), MED does not require predetermined weights to combine individual stage efficiencies. However, if there are external inputs to the second stage, and/or some outputs leave the first stage and do not become inputs to the second stage, or if we assume variable returns to scale (VRS), MED has limited capability to address these extensions. Alternatively, multiplicative efficiency aggregation (MEA), which is highly nonlinear and is impossible to be transformed into a linear programming problem, defines the overall efficiency as a product of stage efficiency scores and can be easily applied to general two-stage network structures. The current study discovers that MEA DEA model for general two-stage networks corresponds to a cone structure in disguise, and can be transformed into the form of second order cone programming (SOCP). Therefore, MEA in two-stage network DEA can be effectively and efficiently solved, regardless of the network structures. We show that AED can also be solved using SOCP and demonstrate that input and output-oriented AED models may not yield the same efficiency scores under CRS. The current research enables us to solve both MEA and AED using SOCP which is considered as effective as linear programming. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Data envelopment analysis (DEA) Multiplicative efficiency aggregation Two-stage second order cone programming

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second order cone programming relaxation for quadratic assignment problems

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OPTIMIZATION METHODS & SOFTWARE 2008年第3期23卷 441-449页

作者： Xia, Yong Beihang Univ Dept Appl Math Beijing Peoples R China

We present a second order cone programming relaxation with O(n(2)) variables for quadratic assignment problems, which provides a lower bound not less than the well-known quadratic programming bound. It is further stre... 详细信息

关键词： second order cone programming quadratic assignment problem quadratic programming bound

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Peak-to-average power ratio reduction using second order cone programming based tone reservation for terrestrial digital video broadcasting systems

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IET COMMUNICATIONS 2009年第7期3卷 1250-1261页

作者： Mahafeno, I. M. Louet, Y. Helard, J. -F. INSA Rennes CNRS UMR 6164 Inst Elect & Telecommun Rennes F-35043 Rennes France SUPELEC F-35576 Cesson Sevigne France

High peak-to-average power ratio (PAPR) is a critical issue in any multicarrier systems using orthogonal frequency division multiplexing, as terrestrial digital video broadcasting (DVB). It can result in low power efficiency and large performance degradation of systems, due to the nonlinearity of high-power amplifier (HPA). A PAPR reduction method based on tone reservation technique with second-order cone programming (SOCP) approach in terrestrial DVB systems is proposed. The authors first demonstrate the superiority of the SOCP optimisation algorithm compared with an iterative gradient-based algorithm, using the current DVB-T parameters: significant PAPR reduction gains can be achieved with only a very small set of subcarriers in the useful bandwidth, making the proposed method more promising in terms of spectral efficiency. Moreover, the proposed solution presents a very good trade-off between PAPR reduction gain and mean transmitted power increase. An overall study, taking into account the limitation of the power level of the dedicated subcarriers and the evaluation of the performances in presence of a nonlinear HPA, is presented. These performances are given in terms of adjacent channel power ratio and bit error rate. The resulting PAPR reduction gain demonstrates that the relevance of the proposed method for the future DVB-T standard is straightforward.

关键词： digital video broadcasting second order cone programming Modulation and coding methods high-power amplifier terrestrial digital video broadcasting systems power amplifiers orthogonal frequency division multiplexing OFDM modulation tone reservation Radio and television broadcasting Optimisation techniques peak-to-average power power ratio reduction quadratic programming

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Learning the optimal kernel for Fisher discriminant analysis via second order cone programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第3期203卷 692-697页

作者： Khemchandani, Reshma Jayadeva Chandra, Suresh Indian Inst Technol Dept Math New Delhi 110016 India IBM India Res Lab Inst Area Vasant Kunj New Delhi 110070 India

Kernel Fisher discriminant analysis (KFDA) is a popular classification technique which requires the user to predefine an appropriate kernel. Since the performance of KFDA depends on the choice of the kernel, the problem of kernel selection becomes very important. In this paper we treat the kernel selection problem as an optimization problem over the convex set of finitely many basic kernels, and formulate it as a second order cone programming (SOCP) problem. This formulation seems to be promising because the resulting SOCP can be efficiently solved by employing interior point methods. The efficacy of the optimal kernel, selected from a given convex set of basic kernels, is demonstrated on LICI machine learning benchmark datasets. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Fisher discriminant analysis Kernel methods Machine learning Kernel optimization Support vector machines Convex optimization second order cone programming Semidefinite programming

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The Q method for second order cone programming

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COMPUTERS & OPERATIONS RESEARCH 2008年第5期35卷 1510-1538页

作者： Xia, Yu Alizadeh, Farid Inst Stat Math Minato Ku Tokyo 1068569 Japan Rutgers State Univ Dept Management Sci & Informat Syst Piscataway NJ 08855 USA Rutgers State Univ Rutgers Ctr Operat Res Piscataway NJ 08855 USA

We develop the Q method for the second order cone programming problem. The algorithm is the adaptation of the Q method for semidefinite programming originally developed by Alizadeh, Haeberly and Overton [A new primal-dual interior point method for semidefinite programming. In: Proceedings of the fifth SIAM conference on applications of linear algebra, Snowbird, Utah, 1994.] and [Primal-dual interior-point methods for semidefinite programming: convergence rates, stability and numerical results. SIAM Journal on Optimization 1998;8(3):746-68 [electronic].]. We take advantage of the special algebraic structure associated with second order cone programs to formulate the Q method. Furthermore we discuss the convergence properties of the algorithm. Finally, some numerical results are presented. (c) 2006 Elsevier Ltd. All fights reserved.

关键词： second order cone programming infeasible interior point method the Q method

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A second-order cone programming Model for Planning PEV Fast-Charging Stations

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IEEE TRANSACTIONS ON POWER SYSTEMS 2018年第3期33卷 2763-2777页

作者： Zhang, Hongcai Moura, Scott J. Hu, Zechun Qi, Wei Song, Yonghua Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China Univ Calif Berkeley Dept Civil & Environm Engn Berkeley CA 94720 USA Tsinghua Berkeley Shenzhen Inst Smart Grid & Renewable Energy Lab Shenzhen 518055 Peoples R China McGill Univ Desautels Fac Management Montreal PQ H3A 1G5 Canada

This paper studies siting and sizing of plug-in electric vehicle (PEV) fast-charging stations on coupled transportation and power networks. We develop a closed-form model for PEV fast-charging stations' service abilities, which considers heterogeneous PEV driving ranges and charging demands. We utilize a modified capacitated flow refueling location model based on subpaths (CFRLM_SP) to explicitly capture time-varying PEV charging demands on the transportation network under driving range constraints. We explore extra constraints of the CFRLM_SP to enhance model accuracy and computational efficiency. We then propose a stochastic mixed-integer second-order cone programming model for PEV fast-charging station planning. The model considers the transportation network constraints of CFRLM_SP and the power network constraints with ac power flow. Numerical experiments are conducted to illustrate the effectiveness of the proposed method.

关键词： Plug-in electric vehicle charging station planning heterogeneous driving ranges transportation power system second order cone programming

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Free isotropic material optimization via second order cone programming

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COMPUTER-AIDED DESIGN 2019年 115卷 52-63页

作者： Yang, Xingtong Li, Ming Zhejiang Univ State Key Lab CAD & CG Hangzhou Zhejiang Peoples R China

Designing an engineered structure of optimal performance is the ultimate goal of engineering design, and various structural optimization approaches have been proposed. However, previous studies on the topic mainly rely on the single design variable of Young's modulus or density without considering its Poisson's ratio as another key isotropic material parameter, and thus may limit the best design ultimately reached. In the study, the problem of free isotropic material optimization (FIMO) is studied that takes as design variables both Young's modulus and Poisson's ratio at each point of the design domain without constraints on its manufacturability;certain necessary conditions on the material attainability are the only imposed requirements. Global optimum to the FIMO is achieved via rigorously reformulating it as a second order cone programming, to which a global optimum is theoretically verified and numerically trackable;the novel formulation also avoids the challenging singularity issue on void elements. The material dimension of the resulted design can also be reduced to any prescribed number of high fidelity via a hierarchical material clustering algorithm. The generated structure can be taken as benchmark solutions with which other optimized designs can be compared, and to propose novel new product design. Performance of the approach is tested on various 2D examples, in comparison with structures generated via classical topology optimization. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Free isotropic material optimization (FIMO) second order cone programming Poisson's ratio Multi-material Topology optimization

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Green supply chain design with emission sensitive demand: second order cone programming formulation and case study

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OPTIMIZATION LETTERS 2021年第1期15卷 231-247页

作者： Elhedhli, Samir Gzara, Fatma Waltho, Cynthia Univ Waterloo Dept Management Sci Waterloo ON Canada

We propose a novel modeling framework for supply chain network design that models a prevailing trend in consumer choice in which demand is impacted by carbon footprint. To date, the literature lacks models that realistically account for and accurately calculate per unit emissions, i.e., carbon footprint. We develop a profit maximizing model that accounts for emissions at the different stages of the supply chain, locates facilities and selects their technology, and decides on the flow between echelons. To calculate the carbon footprint, fixed emissions are averaged over throughput, which results in a nonlinear optimization problem with fractional terms. To solve it, we provide a mixed integer second order cone programming reformulation. We perform extensive testing of the framework on a realistic case study and carry out detailed analysis. The proposed framework succeeds in capturing the trade-off between lost demand due to a high carbon footprint and investing in environmentally-friendly technology. The framework serves as a tool to induce organizations to invest in green technology and to allow regulating authorities to assess the impact of eco-labeling.

关键词： Green supply chain design second order cone programming Carbon footprint Emission sensitive demand Eco-labels

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