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second-order cone programming for Data-Driven Fluid and Gas Energy Flow With a Tight Reformulation

IEEE TRANSACTIONS ON POWER SYSTEMS 2021年第2期36卷 1652-1655页

作者： Jia, Wenhao Ding, Tao Shahidehpour, Mohammad Xi An Jiao Tong Univ Dept Elect Engn Xian 710049 Peoples R China IIT ECE Dept Chicago IL 60616 USA

The precise fluid and gas energy flow equations (FEFEs) are difficult to formulate due to the uncertain parameters. This paper proposes a data-driven approach to fit the FEFEs by polynomial functions through experimental data. Furthermore, a convex optimization model is set up to find the solution of the FEFEs, and a tight reformulation is proposed to exactly reformulate the proposed model as a second-order cone programming (SOCP) that can be tractably solved. Numerical results on several test systems show the effectiveness of the proposed method.

关键词： Manganese Mathematical model Fluids Pipelines Optimization Resistance programming Fluid and gas energy flow polynomial optimization second-order cone programming tight reformulation

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second-order cone programming relaxation-based multi-period reactive power optimization with VSC-Type HVDC and DFIG 3

Second-order cone programming relaxation-based multi-period ...

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3rd International Conference on Energy Engineering and Environmental Protection (EEEP)

作者： Fan, Shixiong Wang, Wei Han, Wei Wang, Wei Zhang, Peng Shen, Xiaodong Liu, Yan China Elect Power Res Inst Beijing Peoples R China State Grid Gansu Elect Power Co Lanzhou Gansu Peoples R China Sichuan Univ Coll Elect Engn & Informat Technol Chengdu Sichuan Peoples R China

This paper presents a second order cone programming (SOCP) formulation of the dynamic reactive power optimization (DROPF) problem for the voltage source converter (VSC)-based high-voltage direct current (HVDC) transmission network, considering reactive power support of the doubly fed induction generator (DFIG). In this model, the reactive power support of DFIG, VAR compensators, the position of tap-changer and the states of VSC converters are formulated as continuous and discrete decision variables. By using approximation techniques, the original non-convex optimisation model is converted into a mixed-integer second-order cone programming model. Later, the SOCP formulation can be solved using many standard optimization packages. Then a DC system with VSC technology is modelled in the IEEE 30-bus example system. The SOCP formulation of AC-DC DROPF is applied to the modified IEEE 30-bus example system and the results are discussed.

关键词： second-order cone programming

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second-order cone programming (SOCP) techniques for coordinating large-scale robot teams in polygonal environments

Second-order cone programming (SOCP) techniques for coordina...

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7th International Conference on Cooperative Control and Optimization

作者： Derenick, Jason C. Spletzer, John R. Lehigh Univ Bethlehem PA 18015 USA

ISBN: (纸本)9783540743545

In this paper, we present an online optimization approach for coordinating large-scale robot teams in both convex and non-convex polygonal environments. In the former, we investigate the problem of moving a team of m robots from an initial shape to an objective shape while minimizing the total distance the team must travel within the specified workspace. Employing SOCP techniques, we establish a theoretical complexity of O(k(1.5)m(1.5)) for this problem with O(km) performance in practice - where k denotes the number of linear inequalities used to model the workspace. Regarding the latter, we present a multi-phase hybrid optimization approach. In Phase I, an optimal path is generated over an appropriate tessellation of the workspace. In Phase II, model predictive control techniques are used to identify optimal formation trajectories over said path while guaranteeing against collisions with obstacles and workspace boundaries. Once again employing SOCP, we establish complementary complexity measures of O(l(3.5)m(1.5)) and O(l(1.5)m(3.5)) for this problem with O(l(3)m) and O(lm(3)) performance in practice - where l denotes the length of the optimization horizon.

关键词： second-order cone programming

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second-order cone programming based Mars powered descent trajectory planning with obstacle avoidance constraints

Second-order cone programming based Mars powered descent tra...

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IAF Astrodynamics Symposium 2021 at the 72nd International Astronautical Congress, IAC 2021

作者： Long, Jiateng Cui, Pingyuan Zhu, Shengying Xiu, Wenbo Institute of Deep Space Exploration School of Aerospace Engineering China

ISBN: (纸本)9781713843078

Motivated by the excellent real-time performance obtaining optimal solution with the deterministic convergence properties, in recent years, the aerospace community emerges great enthusiasm on both of the research and application field of convex optimization. By transforming the objective optimization problems into proper convex forms, convex optimization has revolutionized the optimal problem solving in different backgrounds such as atmospheric entry, powered descent, rocket ascending, etc. Although the convex optimization has shown great advantages on real-time solving and convergence, the objective problem can only be solved through convex optimization after it is convexified. A lot of optimization problems in aerospace engineering, however, contains non-convex performance index, dynamics and constraints, which severely limits the application of convex optimization. To facilitate the application, techniques such as sequential convex optimization, slack variables have been introduced to deal with highly nonlinear and constrained problems. However, convex optimization based fuel-optimal trajectory planning with obstacle avoidance constraints are remain unsolved. To enhance the onboard real-time replanning capability of the fuel-optimal powered descent trajectory when unexpected hazardous Mars terrain is detected, this paper aims at solving the non-convex obstacle avoidance constraint in Mars powered descent phase through second-order cone programming (SOCP). As illustrated in the literature that geometrically convex trajectory shows excellent performance on avoiding obstacles. However, the non-convex constraint form of geometric convex trajectory is the bottleneck of this problem. To this end, the concept of pseudo-velocity vector and pseudo-acceleration (PA) vector are firstly defined, which are utilized to transform the geometric convex constraint into the angle constraint between these two vectors. Then, by introducing slack variable, this angle constraint can be

关键词： second-order cone programming

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Evacuation network design under road capacity improvement and uncertainty: second-order cone programming reformulations and Benders decomposition

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European Journal of Operational Research 2025年

作者： Hu, Qing-Mi Hu, Shaolong Dong, Zhijie Sasha Song, Yongjia School of Economics and Management Jiangsu University of Science and Technology Zhenjiang212100 China School of Economics and Management Southwest Jiaotong University Chengdu610031 China Key Laboratory of Service Science and Innovation of Sichuan Province Chengdu610031 China School of Transportation Southeast University Nanjing211189 United States Department of Industrial Engineering Clemson University ClemsonSC United States

This work first presents a stochastic shelter location and evacuation planning problem with considering road capacity improvement strategies, in which the fixed setup cost of shelters and the improvement cost of road capacity are subject to a budget limit. To explicitly capture the impact of traffic volumes and road capacity improvement decisions on evacuation time, the Bureau of Public Roads function is employed. The problem is formulated as a non-convex mixed-integer nonlinear program (MINLP) model that is difficult to solve directly since the objective function is a multivariable non-convex nonlinear function. To tackle the non-convex MINLP, second-order cone programming (SOCP) reformulations that can be directly solved by using the state-of-the-art solvers are developed. Furthermore, a Benders decomposition (BD) approach that utilizes duality results of SOCP and employs acceleration strategies associated with valid inequalities, multi-cut, strengthened Benders cuts, knapsack inequalities, and callback routine, is proposed to solve large-scale problems. Moreover, extensive numerical experiments and a real-world case study (a potential hurricane risk zone in Texas, U.S.) are conducted to verify the applicability and effectiveness of the proposed model and solution approaches. Computational results show that the derived reformulations are competitive in dealing with small- and medium-scale problems, whereas BD approach demonstrates the best computational performance in solving large-scale problems. The devised acceleration strategies are effective in improving the computational efficiency of the BD approach. In addition, exerting investment for those shelters and arcs that are close to evacuation regions is useful to reduce the expected total evacuation time. © 2025 Elsevier B.V.

关键词： second-order cone programming

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CHARACTERIZATIONS OF TILT-STABLE MINIMIZERS IN second-order cone programming

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SIAM JOURNAL ON OPTIMIZATION 2019年第4期29卷 3100-3130页

作者： Benko, Matus Gfrerer, Helmut Mordukhovich, Boris S. Johannes Kepler Univ Linz Inst Computat Math A-4040 Linz Austria Wayne State Univ Dept Math Detroit MI 48202 USA

This paper is devoted to the study of tilt stability of local minimizers, which plays an important role in both theoretical and numerical aspects of optimization. This notion has been comprehensively investigated in the unconstrained framework as well as for problems of nonlinear programming with C-2-smooth data. Available results for nonpolyhedral conic programs were obtained only under strong constraint nondegeneracy assumptions. Here we develop an approach of second-order variational analysis, which allows us to establish complete neighborhood and point-based characterizations of tilt stability for problems of second-order cone programming generated by the nonpolyhedral second-order/Lorentz/ice-cream cone. These characterizations are established under the weakest metric subregularity constraint qualification condition.

关键词： second-order variational analysis second-order cone programming tilt stability normal cone mappings graphical derivatives C2-cone reducibility metric subregularity

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Naive constant rank-type constraint qualifications for multifold second-order cone programming and semidefinite programming

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OPTIMIZATION LETTERS 2022年第2期16卷 589-610页

作者： Andreani, R. Haeser, G. Mito, L. M. Ramirez, H. Santos, D. O. Silveira, T. P. Univ Estadual Campinas Dept Appl Math Campinas SP Brazil Univ Sao Paulo Dept Appl Math Sao Paulo SP Brazil Univ Chile Dept Ingn Matemat Santiago Chile Univ Chile Ctr Modelamiento Matemat CNRS UMI 2807 Santiago Chile Univ Fed Sao Paulo Inst Sci & Technol Sao Jose Dos Campos SP Brazil

The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used for sensitivity analysis, global convergence of first- and second-order algorithms, and for computing the directional derivative of the value function. In this paper we discuss naive extensions of constant rank-type constraint qualifications to second-order cone programming and semidefinite programming, which are based on the Approximate-Karush-Kuhn-Tucker necessary optimality condition and on the application of the reduction approach. Our definitions are strictly weaker than Robinson's constraint qualification, and an application to the global convergence of an augmented Lagrangian algorithm is obtained.

关键词： Constraint qualifications Optimality conditions second-order cone programming Semidefinite programming Global convergence

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A new formulation for second-order cone programming support vector machine

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INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2024年第3期15卷 1101-1111页

作者： Zong, Zemin Mu, Xuewen Xidian Univ Sch Math & Stat Xian 710071 Shanxi Peoples R China

A new second-order cone programming (SOCP) formulation inspired by the soft-margin linear programming support vector machine (LP-SVM) formulation and cost-sensitive framework is proposed. Our proposed method maximizes the slack variables related to each class by appropriately relaxing the bounds on the VC dimension using the l(infinity)-norm, and penalizes them using the corresponding regularization parametrization to control the trade-off between margin and slack variables. The proposed method has two main advantages: firstly, a flexible classifier is constructed that extends the advantages of the soft-margin LP-SVM problem to the second-order cone;secondly, due to the elimination of a conic restriction, only two SOCP problems containing second-order cone constraints need to be solved. Thus similar results to the SOCP-SVM problem are obtained with less calculational effort. Numerical experiments show that our method achieves the better classification performance than the conventional SOCP-SVM formulations and standard linear SVM formulations.

关键词： second-order cone programming Support vector machine Linear programming SVM

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A two-stage coordinated line loss reduction model based on elephant herding optimization and second-order cone programming

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ENERGY REPORTS 2023年 9卷 930-938页

作者： Wang, Haoyu Fu, Hui Zhou, Cheng Fei, Juntao Zhang, Liang Nanjing Inst Technol Nanjing 211167 Peoples R China State Grid Jiangsu Elect Power Co Ltd Res Inst Nanjing 211103 Peoples R China State Grid Elect Power Res Inst NARI TECHNOL CO L Nanjing 211000 Peoples R China

Aiming at the problem of high line loss caused by the access station of distributed generation (DG), a two-stage coordinated line loss reduction model based on elephant herding optimization (EHO) and second-order cone programming (SOCP) was put forward by using static var generators (SVG) and energy storage system (ESS) to reduce the line loss from reactive and active power aspects, respectively. Firstly, based on the elephant herding optimization, the location model of distributed generation, SVG and ESS was constructed and determined. On this basis, a cooperative line loss reduction model is proposed, which takes into account multiple line loss reduction methods, such as SVG reactive power compensation device and energy storage. By properly dealing with power flow constraints of distributed generation, the influence of operation control mode of distributed generation on optimal distribution and line loss reduction is precisely explained. The constraint is transformed into a second-order cone programming problem by using second-order cone relaxation. In this way, the coordinated reduction of line loss is realized, and the goal of line loss minimization and voltage stability maximization is achieved. Finally, a practical station is taken as an example to verify the correctness of the proposed model and algorithm and the effectiveness of the proposed method. (c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Distributed generation Energy storage system Static var generator Elephant herding optimization second-order cone programming

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A trust region SQP-filter method for nonlinear second-order cone programming

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2012年第12期63卷 1569-1576页

作者： Zhang, Xiangsong Liu, Zhenhua Liu, Sanyang Xian Technol Univ Dept Appl Math Xian 710032 Shaanxi Peoples R China Univ Elect Sci & Technol China Network & Data Secur Key Lab Sichuan Prov Chengdu 611731 Sichuan Peoples R China Xidian Univ Dept Math Xian 710071 Shaanxi Peoples R China

In this paper, we consider the nonlinear second-order cone programming problem. By combining an SQP method and filter technique, we present a trust region SQP-filter method for solving this problem. The proposed algorithm avoids using the classical merit function with penalty term. Furthermore, under standard assumptions, we prove that the iterative sequence generated by the presented algorithm converges globally. Preliminary numerical results indicate that the algorithm is promising. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： second-order cone programming Sequence quadratic programming method Filter technique Trust region method Global convergence

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