Absolute value equations (AVE) provide a useful tool for optimization as they subsume many mathematical programming problems. However, in some applications, it is difficult to determine the exact values of the problem...
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Absolute value equations (AVE) provide a useful tool for optimization as they subsume many mathematical programming problems. However, in some applications, it is difficult to determine the exact values of the problem data and there may be some certain errors. Finding a solution for AVE based on erroneous data using existing approaches might yield a meaningless solution. In this paper, robust optimization, which represents errors in the problem data, is used. We prove that a robust solution can be obtained by solving a robust counterpart problem, which is equivalent to a secondorder cone program. The results also show that robust solutions can significantly improve the performance of solutions, especially when the size of errors in the problem is large.
In this paper, we investigate the energy system design problems with the multi-generation technologies, i.e., simultaneous generation of multiple types of energy. Our results illustrate the economic value of multi-gen...
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In this paper, we investigate the energy system design problems with the multi-generation technologies, i.e., simultaneous generation of multiple types of energy. Our results illustrate the economic value of multi-generation technologies to reduce spatio-temporal demand uncertainty by risk pooling both within and across different facilities. Published by Elsevier B.V.
Insurance and reinsurance are important tools of risk management. A well- designed (re)insurance strategy can help individuals and institutions to effectively adjust its risk position to match its risk appetite while ...
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Insurance and reinsurance are important tools of risk management. A well- designed (re)insurance strategy can help individuals and institutions to effectively adjust its risk position to match its risk appetite while meeting other targets such as profitability. Thus, optimal (re)insurance design has been a popular research area during the last fifty years. The first contribution investigates the optimal reinsurance contract from the per- spective of an insurer who would like to minimise its risk exposure under Solvency II. Under this regulatory framework, the insurer is exposed to the retained risk, reinsur- ance premium and change in the risk margin requirement as a result of reinsurance. Depending on how the risk margin corresponding to the reserve risk is calculated, two optimal reinsurance problems are formulated. We show that the optimal reinsurance policy can be in the form of two layers. Further, numerical examples illustrate that the optimal two-layer reinsurance contracts are only slightly different under these two methodologies. In the second contribution, numerical optimisation methods that are practically implementable and solvable are discussed with actuarial applications. The efficiency of these methods is extremely good for some well-behaved convex problems, such as the second-orderconic Problems. Specific numerical solutions are provided in or- der to better explain the advantages of appropriate numerical optimisation methods chosen to solve various risk transfer problems. The stability issues are also investi- gated together with a case study performed for an insurance group that aims capital efficiency across the entire organisation. The next two contributions aim to identify a robust optimal insurance contract that is not sensitive to the chosen risk distribution. The first of the two contributions focuses on the classical robust optimisation models, namely the worst-case and the worst-regret model, which have been already investigated in literat
The increasing integration of distributed generation introduces severe challenges to the secure and economical operation of multi-microgrids (MMGs). Therefore, an accurate and timely estimation of secure ranges for dy...
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The increasing integration of distributed generation introduces severe challenges to the secure and economical operation of multi-microgrids (MMGs). Therefore, an accurate and timely estimation of secure ranges for dynamic interchange adjustments is necessary for microgrid operators. This study develops a new modeling framework for estimating the interchange capability between MMGs and a distribution network (DN) to increase the situation awareness of the microgrid operator. This framework contains a two models, namely, (1) the proposed prediction model, which considers the economical operation, the robustness of power interchange, and the uncertainty of renewable resources on a microgrid level to obtain the operation states and predicted interchange capabilities, and (2) the correction model, which determines the available interchange capabilities (AICs) while considering the effect of security constraints and spinning reserve on the DN level. AICs ensure the control flexibility and security of micro grids. The approach based on model predictive control is used in this framework to optimize the system operation on the microgrid and DN levels. The point estimation method and second-order conic programming are used to solve the two-level model to guarantee a globally optimal solution and improved computational efficiency. Finally, a distribution system with multiple microgrids is applied to prove the effectiveness of the proposed framework. (C) 2017 Elsevier B.V. All rights reserved.
We study the trust-region subproblem (TRS) of minimizing a nonconvex quadratic function over the unit ball with additional conic constraints. Despite having a nonconvex objective, it is known that the classical TRS an...
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We study the trust-region subproblem (TRS) of minimizing a nonconvex quadratic function over the unit ball with additional conic constraints. Despite having a nonconvex objective, it is known that the classical TRS and a number of its variants are polynomial-time solvable. In this paper, we follow a second-order cone (SOC) based approach to derive an exact convex reformulation of the TRS under a structural condition on the conic constraint. Our structural condition is immediately satisfied when there are no additional conic constraints, and it generalizes several such conditions studied in the literature. As a result, our study highlights an explicit connection between the classical nonconvex TRS and smooth convex quadratic minimization, which allows for the application of cheap iterative methods such as Nesterov's accelerated gradient descent, to the TRS. Furthermore, under slightly stronger conditions, we give a low-complexity characterization of the convex hull of the epigraph of the nonconvex quadratic function intersected with the constraints defining the domain without any additional variables. We also explore the inclusion of additional hollow constraints to the domain of the TRS, and convexification of the associated epigraph.
Probability constraints play a key role in optimization problems involving uncertainties. These constraints request that an inequality system depending on a random vector has to be satisfied with a high enough probabi...
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Probability constraints play a key role in optimization problems involving uncertainties. These constraints request that an inequality system depending on a random vector has to be satisfied with a high enough probability. In specific settings, copulae can be used to model the probabilistic constraints with uncertainty on the left-hand side. In this paper, we provide eventual convexity results for the feasible set of decisions under local generalized concavity properties of the constraint mappings and involved copulae. The results cover all Archimedean copulae. We consider probabilistic constraints wherein the decision and random vector are separated, i.e. left/right-hand side uncertainty. In order to solve the underlying optimization problem, we propose and analyse convergence of a regularized supporting hyperplane method: a stabilized variant of generalized Benders decomposition. The algorithm is tested on a large set of instances involving several copulae among which the Gaussian copula. A Numerical comparison with a (pure) supporting hyperplane algorithm and a general purpose solver for non-linear optimization is also presented.
With a higher level of electric vehicle load penetrated in the distribution network, reconfiguration could be employed to minimize energy losses. Based on a second-order conic programming formulation, an improved set ...
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ISBN:
(纸本)9781467380409
With a higher level of electric vehicle load penetrated in the distribution network, reconfiguration could be employed to minimize energy losses. Based on a second-order conic programming formulation, an improved set of network radiality constraints is proposed using power-flow based network connectivity conditions. This proves to be a computationally more efficient method compared to the spanning tree constraints. To incorporate electric vehicle charging in the reconfiguration model, two aggregated charging strategies are proposed: the arbitrary delay and the peak-avoiding delay. The decision of delay hours is formulated as constraints and co-optimized into the reconfiguration model. Case study on the IEEE 33-bus system illustrates the performance of the proposed model and the effectiveness of the proposed charging strategy.
The paper considers solving of linear programming problems with p-orderconic constraints that are related to a certain class of stochastic optimization models with risk objective or constraints. The proposed approach...
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The paper considers solving of linear programming problems with p-orderconic constraints that are related to a certain class of stochastic optimization models with risk objective or constraints. The proposed approach is based on construction of polyhedral approximations for p-order cones, and then invoking a Benders decomposition scheme that allows for efficient solving of the approximating problems. The conducted case study of portfolio optimization with p-orderconic constraints demonstrates that the developed computational techniques compare favorably against a number of benchmark methods, including second-order conic programming methods. (C) 2009 Elsevier B.V. All rights reserved.
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