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second-order cone programming models for the unitary weighted Weber problem and for the minimum sum of the squares clustering problem

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2025年第2期32卷 961-972页

作者： Linhares, Marcella Braga de Assis Pinto, Renan Vicente Maculan, Nelson Negreiros, Marcos Univ Fed Rio De Janeiro PESC COPPE Rio de Janeiro Brazil Fed Rural Univ Rio Janeiro Dept Math Rio De Janeiro Brazil Univ Estadual Ceara Sci Comp Lab Fortaleza CE Brazil

In this work, new mixed integer nonlinear optimization models are proposed for two clustering problems: the unitary weighted Weber problem and the minimum sum of squares clustering. The proposed formulations are convex quadratic models with linear and second-order cone constraints that can be efficiently solved by interior point algorithms. Their continuous relaxation is convex and differentiable. The numerical experiments show the proposed models are more efficient than some classical models for these problems known in the literature.

关键词： combinatorial optimization nonlinear programming clustering problem second-order cone programming

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Operational Coordination Optimization of Electricity and Natural Gas Networks Based on Sequential Symmetrical second-order cone programming

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JOURNAL OF MODERN POWER SYSTEMS AND CLEAN ENERGY 2025年第2期13卷 488-499页

作者： Min, Liang Lou, Chengwei Yang, Jin Yu, James Yu, Zhibin Power Grid Dispatching & Control Branch Co NARI Te Nanjing Peoples R China China Agr Univ Coll Informat & Elect Engn Beijing Peoples R China Univ Glasgow Sch Engn Glasgow G12 8QQ Scotland Scottish Power Energy Network Glasgow G2 5AD Scotland Univ Liverpool Dept Mech & Aerosp Engn Liverpool England

The variable and unpredictable nature of renewable energy generation (REG) presents challenges to its large-scale integration and the efficient and economic operation of the electricity network, particularly at the distribution level. In this paper, an operational coordination optimization method is proposed for the electricity and natural gas networks, aiming to overcome the identified negative impacts. The method involves the implementation of bi-directional energy flows through power-to-gas units and gas-fired power plants. A detailed model of the three-phase power distribution system up to each phase is employed to improve the representation of multi-energy systems to consider real-world end-user consumption. This method allows for the full consideration of unbalanced operational scenarios. Meanwhile, the natural gas network is modelled and analyzed with steady-state gas flows and the dynamics of the line pack in pipelines. The sequential symmetrical second-order cone programming (SS-SOCP) method is employed to facilitate the simultaneous analysis of three-phase imbalance and line pack while accelerating the solution process. The efficacy of the operational coordination optimization method is demonstrated in case studies comprising a modified IEEE 123-node power distribution system with a 20-node natural gas network. The studies show that the operational coordination optimization method can simultaneously minimize the total operational cost, the curtailment of installed REG, the voltage imbalance of three-phase power system, and the overall carbon emissions.

关键词： Natural gas Power systems Pipelines Electricity Optimization Mathematical models Load flow programming Numerical models Power system dynamics Operational coordination multi-energy system power-to-gas electricity network natural gas network second-order cone programming

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A second-order cone programming-based microgrid bidding strategy considering real-time market price correlation

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ELECTRICAL ENGINEERING 2025年 1-14页

作者： El-Meligy, Mohammed A. Sharaf, Mohamed Alnowibet, Khalid A. Abdelgawad, Abdelatty E. King Saud Univ Adv Mfg Inst POB 800 Riyadh 11421 Saudi Arabia King Saud Univ Coll Sci Stat & Operat Res Dept Riyadh 11451 Saudi Arabia King Saud Univ Coll Engn Ind Engn Dept POB 800 Riyadh 11421 Saudi Arabia

This study establishes a non-deterministic microgrid bidding strategy methodology participating in a day-ahead energy market. In this regard, a stochastic programming-based model is mathematically constructed, fully considering the uncertainty of day-ahead market prices, electricity demand, and renewable generation by creating several scenarios. The real-time electricity market is also considered, where the real-time price uncertainty is modeled using robust optimization. Even though robust optimization has already been employed to model real-time price uncertainty, the correlation among real-time prices at different hours is neglected. Thus, how real-time price correlation affects the optimal microgrid bidding strategy remains unclear. This study develops a novel mathematical model that captures real-time price correlations by constructing an ellipsoidal uncertainty set. In this context, unlike the current approaches in which the real-time price deviation ranges are modeled as constants at each hour, they are assumed to lie within a prespecified ellipsoidal uncertainty set. In doing so, a mixed-integer second-order cone programming problem is created, which existing solving methods can efficiently handle. The presented scheme is applied to a typical microgrid, and the efficiency and excellence of the presented framework are validated by comparing numerical results with traditional models.

关键词： Correlation Ellipsoidal uncertainty set Microgrid bidding strategy Robust optimization second-order cone programming Stochastic programming

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A second-order sequential optimality condition for nonlinear second-order cone programming problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2025年第3期90卷 911-939页

作者： Fukuda, Ellen H. Okabe, Kosuke Kyoto Univ Grad Sch Informat Sakyo KuYoshida Honmachi Kyoto Kyoto 6068501 Japan

In the last two decades, the sequential optimality conditions, which do not require constraint qualifications and allow improvement on the convergence assumptions of algorithms, had been considered in the literature. It includes the work by Andreani et al. (IMA J Numer Anal 37:1902-1929, 2017), with a sequential optimality condition for nonlinear programming, that uses the second-order information of the problem. More recently, Fukuda et al. (Set-Valued Var Anal 31:15, 2023) analyzed the conditions that use second-order information, in particular for nonlinear second-order cone programming problems (SOCP). However, such optimality conditions were not defined explicitly. In this paper, we propose an explicit definition of approximate-Karush-Kuhn-Tucker 2 (AKKT2) and complementary-AKKT2 (CAKKT2) conditions for SOCPs. We prove that the proposed AKKT2/CAKKT2 conditions are satisfied at local optimal points of the SOCP without any constraint qualification. We also present two algorithms that are based on augmented Lagrangian and sequential quadratic programming methods and show their global convergence to points satisfying the proposed conditions.

关键词： Optimality conditions second-order optimality second-order cone programming Conic optimization

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AUBIN PROPERTY AND STRONG REGULARITY ARE EQUIVALENT FOR NONLINEAR second-order cone programming

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SIAM Journal on Optimization 2025年第2期35卷 712-738页

作者： Chen, Liang Chen, Ruoning Sun, Defeng Zhu, Junyuan School of Mathematics Hunan University Changsha China Department of Mathematical Sciences Tsinghua University Beijing China Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Hong Kong

This paper solves a fundamental open problem in variational analysis on the equivalence between the Aubin property and the strong regularity for nonlinear second-order cone programming (SOCP) at a locally optimal solution. We achieve this by introducing a reduction approach to the Aubin property characterized by the Mordukhovich criterion and a lemma of alternative choices on cones to replace the S-lemma used in Outrata and Ramírez [SIAM J. Optim., 21 (2011), pp. 789-823] and Opazo, Outrata, and Ramírez [SIAM J. Optim., 27 (2017), pp. 2143-2151], where the same SOCP was considered under the strict complementarity condition except for possibly only one block of constraints. As a byproduct, we also offer a new approach to the well-known result of Dontchev and Rockafellar [SIAM J. Optim., 6 (1996), pp. 1087-1105] on the equivalence of the two concepts in conventional nonlinear programming. © 2025 Society for Industrial and Applied Mathematics.

关键词： second-order cone programming

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second-order cone programming formulations for a class of problems in structural optimization

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2010年第1-6期40卷 365-380页

作者： Makrodimopoulos, Athanasios Bhaskar, Atul Keane, Andy J. Univ Southampton Sch Engn Sci Southampton Hants England

This paper provides efficient and easy to implement formulations for two problems in structural optimization as second-order cone programming (SOCP) problems based on the minimum compliance method and derived using the principle of complementary energy. In truss optimization both single and multiple loads (where we optimize the worst-case compliance) are considered. By using a heuristic which is based on the SOCP duality we can consider a simple ground structure and add only the members which improve the compliance of the structure. It is also shown that thickness optimization is a problem similar to truss optimization. Examples are given to illustrate the method developed in this paper.

关键词： Structural optimization Truss optimization Thickness optimization second-order cone programming

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second-order cone programming for solving unit commitment strategy of thermal generators

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ENERGY CONVERSION AND MANAGEMENT 2013年 76卷 20-25页

作者： Yuan, Xiaohui Tian, Hao Zhang, Shuangquan Ji, Bin Hou, Yanhong Huazhong Univ Sci & Technol Sch Hydropower & Informat Engn Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Sch Energy & Power Engn Wuhan 430074 Peoples R China

The short-term unit commitment (UC) problem of hydrothermal generation systems is a mixed-integer nonlinear programming (MINLP), which is difficult to solve efficiently, especially for large-scale instances. The perspective relaxation (PR) is an effective approach to constructing tight approximations to MINLP with semi-continuous variables. In this paper, the PR of UC problem is formulated as a mixed integer second-order cone programming (SOCP) model because the quadratic polynomial cost function of the UC problem is SOCP-representable. The proposed model is implemented by using the commercial optimization software IBM CPLEX 12.4. Extensive numerical studies have been conducted to verify the advantages of our proposed method. Instances of the test system vary from 10 to 1000 units. Our results indicate that the proposed method performs better than the existing methods in terms of production cost savings and faster computational times, especially for large systems. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Mixed-integer nonlinear programming second-order cone programming Separable convex function Unit commitment

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second-order cone programming approaches to static shakedown analysis in steel plasticity

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OPTIMIZATION METHODS & SOFTWARE 2005年第1期20卷 25-52页

作者： Bisbos, CD Makrodimopoulos, A Pardalos, PM Aristotle Univ Thessaloniki Dept Civil Engn Inst Steel Struct GR-54124 Thessaloniki Greece Univ Oxford Dept Engn Sci Oxford OX1 3PJ England Univ Florida Dept Ind & Syst Engn Ctr Appl Optimizat Gainesville FL 32611 USA

The finite element method discretized static shakedown analysis of steel constructions leads to large, sparse convex optimization problems. Under the von Mises yield criterion, they lead to second-order cone programming problems, for which the most appropriate techniques are Interior Point Methods. Various approaches exploiting the specific characteristics of the shakedown problems are presented and discussed.

关键词： shakedown plasticity second-order cone programming large sparse optimization FEM

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second-order cone programming formulation for consolidation analysis of saturated porous media

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COMPUTATIONAL MECHANICS 2016年第1期58卷 29-43页

作者： Zhang, Xue Sheng, Daichao Sloan, Scott W. Krabbenhoft, Kristian Univ Newcastle ARC Ctr Excellence Geotech Sci & Engn Newcastle NSW 2300 Australia

In this paper, the incremental problem for consolidation analysis of elastoplastic saturated porous media is formulated and solved using second-order cone programming. This is achieved by the application of the Hellinger-Reissner variational theorem, which casts the governing equations of Biot's consolidation theory as a min-max optimisation problem. The min-max problem is then discretised using the finite element method and converted into a standard second-order cone programming problem that can be solved efficiently using modern optimisation algorithms (such as the primal-dual interior-point method). The proposed computational formulation is verified against a number of benchmark examples and also applied to simulate the construction of a road embankment on soft clay.

关键词： Saturated porous media Consolidation second-order cone programming Mathematical programming

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second-order cone programming for Optimal Power Flow in VSC-Type AC-DC Grids

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IEEE TRANSACTIONS ON POWER SYSTEMS 2013年第4期28卷 4282-4291页

作者： Baradar, Mohamadreza Hesamzadeh, Mohammad Reza Ghandhari, Mehrdad KTH Royal Inst Technol Sch Elect Engn Dept Elect Power Syst SE-10044 Stockholm Sweden

This paper presents a second order cone programming (SOCP) formulation of the optimal power flow problem for AC-DC systems with voltage source converter (VSC) technology. Approximation techniques have been used to derive the SOCP formulation of the AC-DC OPF problem. Later, the SOCP formulation can be solved using the interior point method (IPM) by considering the limits on AC-DC grid. The accuracy of SOCP formulation of AC OPF has been proven with numerical examples using IEEE 14-bus, IEEE 30-bus, and IEEE 57-bus example systems. The results of the SOCP formulation are compared with available commercial software. Then a DC system with VSC technology is modeled in the IEEE 30-bus example system. The SOCP formulation of AC-DC OPF is applied to the modified IEEE 30-bus example system and the results are discussed. The limitations of derived SOCP formulation are also discussed.

关键词： AC-DC optimal power flow multi-terminal HVDC systems second-order cone programming

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