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A penalty-type method for solving inverse optimal value problem in second-order conic programming

APPLIED NUMERICAL MATHEMATICS 2024年 198卷 419-427页

作者： Lu, Yue Dong, Zheng-Peng Hu, Zhi-Qiang Ma, Hong-Min Xue, Dong-Yang Tianjin Normal Univ Sch Math Sci Tianjin 300387 Peoples R China Tianjin Univ Commerce Sch Mech Engn Tianjin 300134 Peoples R China

This paper aims to consider a type of inverse optimal value problem in second -order conic programming, in which the parameter in its objective function needs to be adjusted under a given class that makes the corresponding optimal objective value closest to a target value. This inverse problem can be reformulated as a minimization problem with some second -order cone complementarity constraints. To tackle these bilinear constraints, we apply a penalty -type method and show that the associated penalty term is exact, which avoids the hurdles of penalty -type methods in the update strategy of the penalty parameter. Numerical results show that our method is suitable to solve the given inverse optimal value problem under different metric distances between the optimal value of the forward problem and a target objective counterpart.

关键词： Inverse optimal value problem second-order conic programming Penalty-type method

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ON second-order conic programming DUALS FOR ROBUST CONVEX QUADRATIC OPTIMIZATION PROBLEMS

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2023年第11期19卷 8114-8128页

作者： Zhang, Huan Sun, Xiangkai Li, Genghua Chongqing Technol & Business Univ Coll Math & Stat Chongqing 400067 Peoples R China

. In this paper, we deal with second-order conic programming (SOCP) duals for a robust convex quadratic optimization problem with uncertain data in the constraints. We first introduce a SOCP dual problem for this robust convex quadratic optimization problem with polytopic uncertain sets. Then, we obtain a zero duality gap result between this robust convex quadratic optimization problem and its dual problem in terms of a new robust type characteristic cone constraint qualification. We also construct a SOCP dual problem for this robust convex quadratic optimization problem with norm-constrained uncertain sets and obtain the corresponding zero duality gap result between them. Moreover, some numerical examples are given to explain the obtained results.

关键词： Convex optimization quadratic optimization robust optimization second-order conic programming duality

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Distributionally robust portfolio optimization with second- order stochastic dominance based on wasserstein metric

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INFORMATION SCIENCES 2022年 613卷 828-852页

作者： Hosseini-Nodeh, Zohreh Khanjani-Shiraz, Rashed Pardalos, Panos M. Univ Tabriz Fac Math Stat & Comp Sci Tabriz Iran Univ Florida Ctr Appl Optimizat Ind & Syst Engn Gainesville FL USA

In portfolio optimization, we may be dealing with misspecification of a known distribution, that stock returns follow *** unknown true distribution is considered in terms of a Wasserstein-neighborhood of P to examine the tractable formulations of the portfolio selection problem. This study considers a distributionally robust portfolio optimization problem with an ambiguous stochastic dominance constraint by assuming the unknown distribution of asset returns. The objective is to maximize the worst-case expected return and subject to an ambiguous second-order stochastic dominance constraint. The expected return robustly stochastically dominates the benchmark in the second order over all pos-sible distributions within an ambiguity set. It is also shown that the Wasserstein-moment ambiguity set-based distributionally robust portfolio optimization can be reduced to a semidefinite program and second-order conic programming. We use a cutting plane to solve our second-order stochastic dominance constraint portfolio optimization problem with ambiguity sets based on the Wasserstein metric. Then we decompose this class of dis-tributionally robust portfolio optimization into semi-infinite programming and apply the cutting surface method to solve *** captured optimization programs are applied to real-life data for more efficient comparison. The problems are examined in depth using the optimal solutions of the optimization programs based on the different setups.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Wasserstein metric Portfolio optimization Semidefinite programming second-order stochastic dominance second-order conic programming Ambiguity Semi-infinite programming Cutting surface method

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Analysis of the Precision of a second-order conic Model to Solve the Optimal Power Dispatch Problem in Electric Power Systems

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JOURNAL OF CONTROL AUTOMATION AND ELECTRICAL SYSTEMS 2021年第5期32卷 1356-1364页

作者： Yamaguti, Lucas do Carmo Home-Ortiz, Juan M. Pourakbari-Kasmaei, Mahdi Sanches Mantovani, Jose Roberto Sao Paulo State Univ Dept Elect Engn Ilha Solteira SP Brazil Aalto Univ Dept Elect Engn & Automat Espoo Finland

This paper presents in-depth comparative analyses of nonlinear nonconvex programming (NLNCP) and second-order conic programming (SOCP) models to solve the optimal power flow problem in electric power systems. For comparative purposes, two objective functions are considered (1) minimization of the active power generation costs and (2) minimization of the active power losses in the transmission branches. The robustness and precision of the NLNCP and SOCP models are analyzed and discussed considering the feasibility of the active and reactive power balance constraints and the values of the objective functions. The obtained operational points are verified through the solution of the AC power flow problem using the Newton-Raphson method. For both models, numerical experiments show consistent active power dispatch;however, limit violations in the reactive power generation limits are observed in the solutions obtained by the SOCP model. To address this issue, two variations in the formulation of the SOCP model are proposed (1) considering a penalty factor in the generation of reactive energy and (2) considering a minimum resistance in branches of the power system that have resistance equal to zero. The solution of these modified SOCP models can eliminate or significantly reduce reactive power dispatch limit violations.

关键词： Convex optimization Nonlinear programming Optimal active and reactive power dispatch second-order conic programming

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Economic/Environmental Optimal Power Flow Using a Multiobjective Convex Formulation

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ENERGIES 2023年第12期16卷 4651页

作者： Yamaguti, Lucas do Carmo Home-Ortiz, Juan Manuel Pourakbari-Kasmaei, Mahdi Mantovani, Jose Roberto Sanches Sao Paulo State Univ Dept Elect Engn BR-15385 Ilha Solteira Brazil Aalto Univ Dept Elect Engn & Automat Espoo 01250 Finland

This paper addresses the problem of economic/environmental optimal power flow with a multiobjective formulation using a second-order conic programming (SOCP) optimization model. This problem formulation considers renewable energy sources (RES), fossil-fuel-based power generation units, and voltage control. The proposed SOCP model is a stochastic scenario-based approach to deal with RES and load behavior uncertainties. An e-constrained algorithm is used to handle the following three objective functions: (1) the costs of power generation, (2) active power losses in the branches, and (3) the emission of pollutant gases produced by fossil-fuel-based power generation units. For comparative purposes, the SOCP model is also presented using a linearized formulation, and numerical results are presented using a 118-bus system. The results confirm that changing the energy matrices directly affects the cost of objective functions. Additionally, using a linearized SOCP model significantly reduces reactive power violation in the generation units when compared to the nonlinearized SOCP model, but also increases the computational time consumed.

关键词： & epsilon -constrained algorithm emission pollutant gasses multiobjective optimization optimal power flow renewable energy sources second-order conic programming

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A multi-objective fuzzy facility location problem with congestion and priority for drone-based emergency deliveries

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COMPUTERS & INDUSTRIAL ENGINEERING 2023年第1期179卷

作者： Wang, Xin Zhao, Jiemin Cheng, Chun Qi, Mingyao Tsinghua Univ Dept Ind Engn Beijing 100084 Peoples R China Tsinghua Univ Shenzhen Int Grad Sch Logist & Transportat Div Shenzhen 518055 Peoples R China Dongbei Univ Finance & Econ Inst Supply Chain Analyt Dalian 116025 Peoples R China

Emergency medical service (EMS) plays an essential role in modern emergency and health systems;however, the delivery service via traditional ground vehicles faces enormous challenges, e.g., traffic congestion and poor road conditions, especially for time-critical products. Fortunately, drones provide an alternative solution for EMS due to faster speed, fewer road restrictions, and fewer workforce requirements, compared to ground vehicles. This paper develops a drone-based queuing-location model with stochastic demands and congestion for EMS, where drones perform as mobile servers with a generally distributed service time. In practice, delivery decisions are often made in the presence of imprecise information, and customer requests often have different priorities. However, to our best knowledge, limited research has addressed these issues. Thus, this paper employs fuzzy theory to cope with the vague drone endurance and demand arrival rate under a priority queuing strategy. A multi-objective optimization approach is adopted to balance the total cost, system efficiency, and equitable response time. As the resulting model is challenging to solve, we apply chance-constrained, second -order conic, fuzzy, and weighted goal programming approaches to recast the model as a crisp mixed-integer second-order conic program, which can be efficiently solved via off-the-shelf solvers. Results based on a case study show that our method can help decision-makers to better balance various objectives, make more flexible decisions with desirable fuzzy degrees, and significantly improve the service level of high priority demands for EMS.

关键词： Facility location Drone delivery Queuing Fuzzy programming second-order conic programming Weighted goal programming

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Feasible Point Pursuit Based Sequential Convex Approximation of Optimal Power Flow

Feasible Point Pursuit Based Sequential Convex Approximation...

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IEEE-Power-and-Energy-Society General Meeting (PESGM)

作者： Tiwari, Anamika Mohapatra, A. Sahoo, S. R. Indian Inst Technol Kanpur Dept Elect Engn Kanpur 208016 Uttar Pradesh India

ISBN: (纸本)9781665405072

Optimal Power Flow (OPF) is of paramount importance for the operation of the power network. However, the non-convexity of ACOPF poses convergence issues and limits its application in day to day operation. Therefore, a convex model is needed that gives guaranteed convergence and feasible solution. Among the existing convex OPF models, second-order conic programming (SOCP) is more efficient. However, the exact SOCP formulation of ACOPF has non-convex arctangent constraints. These constraints are generally either ignored or approximated to solve the relaxed and convex SOCP formulation of ACOPF. Consequently, retrieving a unique and feasible set of bus voltage phasors for ACOPF of meshed power networks is a challenge. Thus, this paper proposes a novel approach to recover a unique and feasible ACOPF solution from its convex formulation. The alternate difference of convex functions is used to reformulate the arctangent constraints. The proposed formulation is solved by a modified inner approximation technique such as Feasible Point Pursuit based Sequential Convex Approximation (FPP-SCA) to preserve the feasibility of the solution.

关键词： Sequential Convex Approximation Difference of Convex Functions second-order conic programming Convexity Feasibility Optimal Power Flow

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Optimal Power Flow Solution for Distribution Networks using Quadratically Constrained programming and McCormick Relaxation Technique 21

Optimal Power Flow Solution for Distribution Networks using ...

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21st IEEE International Conference on Environment and Electrical Engineering / 5th IEEE Industrial and Commercial Power Systems Europe (EEEIC/I and CPS Europe)

作者： Javadi, Mohammad Sadegh Gouveia, Clara Sofia Carvalho, Leonel Magalhaes Silva, Ricardo INESC TEC Porto Portugal

ISBN: (纸本)9781665436137

This paper presents a quadratically constrained programming (QCP) model to tackle the optimal power flow (OPF) problem in distribution networks. The proposed model is fast, reliable, and precise enough to be embedded into the multi-emporal power system analysis. The proposed model benefits from a standard QCP to solve the branch active and reactive power flows. The second-order conic programming (SOCP) approach has been applied to address the quadratic constraints. The nonconvex feature of the OPF problem has been relaxed utilizing the McCormick envelopes. To find the minimum current of each branch, the lossless power flow model has been first solved and the obtained results have been considered for solving the OPF problem. The IEEE 33-bus test system has been selected as the benchmark to verify the efficient performance of the proposed OPF model. The simulation study confirms that the McCormick envelopes used in the QCP approach lead to precise results with a very fast convergence time. Overall, the presented model for the OPF can be extended for both planning and operation purposes in distribution system studies.

关键词： Optimal Power Flow Distribution Network Convex Optimization Model second-order conic programming

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Optimal Power Dispatch of Renewable and Non-Renewable Generation through a second-order conic Model 21

Optimal Power Dispatch of Renewable and Non-Renewable Genera...

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21st IEEE International Conference on Environment and Electrical Engineering / 5th IEEE Industrial and Commercial Power Systems Europe (EEEIC/I and CPS Europe)

作者： Yamaguti, Lucas do Carmo Home-Ortiz, Juan M. Pourakbari-Kasmaei, Mahdi Santos, Sergio F. Sanches Mantovani, Jose Roberto Catalao, Joao P. S. Sao Paulo State Univ Dept Elect Engn Ilha Solteira Brazil Aalto Univ Dept Elect Engn & Automat Espoo Finland Portucalense Univ Infante D Henrique Porto Portugal INESC TEC Porto Portugal Univ Porto Fac Engn Porto Portugal

ISBN: (纸本)9781665436137

This work presents an extension of a second-order conic programming model (SOCP) to handle the multi-objective optimal power dispatch problem considering the probabilistic nature of some parameters related to power demand and the renewable energy sources (RES) generation, such as wind speed and solar irradiation level. Three objective functions are considered in this study: 1) costs of RES and non-RES generation;2) active power losses in the transmission system;and, 3) emission pollutant gases produced by fossil fuel-based generating units. The stochastic nature of power demands and RES are developed through a set of representative operational scenarios extracted from historical data and via a scenario reduction technique. The results obtained in the SOCP model are compared with a nonlinear programming (NLP) model to check the robustness and precision of SOCP model. To this, both models are implemented and processed to simulate the optimal flow for the IEEE 57- and 118-bus systems.

关键词： Emission pollutant gases multi-objective optimization optimal power dispatch renewable energy second-order conic programming

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Task assignment in predictive maintenance for free-float bicycle sharing systems

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COMPUTERS & INDUSTRIAL ENGINEERING 2022年第0期169卷

作者： Lu, Lan Zhao, Shichen He, Qiao-Chu Zhu, Ning Univ Sci & Technol China Int Inst Finance Sch Management Hefei 230000 Peoples R China Southern Univ Sci & Technol Sch Business Shenzhen 518055 Peoples R China Tianjin Univ Coll Management & Econ Tianjin 300072 Peoples R China

The growth of Free-Float Bike-Sharing Systems (FFBSs) is heavily impeded by faulty bike maintenance among other operational challenges. In this paper, we aim to improve the efficiency of faulty bike maintenance by predicting faulty bikes in order to make better maintenance assignment decisions. Inspired by industry practice, we identify the role of "black holes" in accurate predictions of faulty bikes: locations with morbidly high faulty rates, which can be characterized using data-driven approaches (clustering and convex hull). Based on the prediction result, we propose two maintenance policies, i.e., the pooling model and the dedicated model, for the faulty bike maintenance assignment problem with the objective of minimizing the sum of maintenance time cost and travel time cost. Finally, we provide a tractable reformulation via linear mix-integer second-order conic programming (SOCP) and conduct a case study with real data. Our analysis identifies the main trade-off between routing efficiency and maintenance efficiency in the different maintenance policies. We find that the pooling policy concentrates on routing efficiency while the dedicated policy emphasizes maintenance efficiency. Moreover, we demonstrate the importance of "black holes" in the prediction of faulty bikes. In the case study, we observe that bikes in "black holes" are about 70% more likely to be faulty than those out of "black holes." We find that the improvement due to prediction is significant even when the prediction is imperfect. In our case study, when prediction accuracy exceeds 65%, we can observe the cost reduction by prediction in the faulty bike maintenance problem.

关键词： Free-float bike-sharing system Faulty bike maintenance problem Predictive decision analytics Dedicated policy second-order conic programming

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