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Optimal Pricing of a Heterogeneous Portfolio for a Given Risk Level

ASTIN Bulletin: The Journal of the IAA 2015年第1期36卷 161-185页

作者： Yaniv Zaks Esther Frostig Benny Levikson Department of Statistics University of Haifa Israel

Consider a portfolio containing heterogeneous risks, where the policyholders’ premiums to the insurance company might not cover the claim payments. This risk has to be taken into consideration in the premium pricing. On the other hand, the premium that the insureds pay has to be fair. This fairness is measured by the distance between the risk and the premium paid. We apply a non-linear programming formulation to find the optimal premium for each class so that the risk is below a given level and the weighted distance between the risk and the premium is minimized. We consider also the dual problem: minimizing the risk level for a given weighted distance between risks and premium.

关键词： Heterogeneous portfolio Positive Definite Matrix non-linear programming dual problem

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High-Fidelity Harmonic Generation in Optical Micro-Resonators Using BFGS Algorithm

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MICROMACHINES 2020年第7期11卷 686-686页

作者： Asirim, Ozum Emre Yolalmaz, Alim Kuzuoglu, Mustafa Middle East Tech Univ Dept Elect & Elect Engn TR-06800 Ankara Turkey Middle East Tech Univ Micro & Nanotechnol Program TR-06800 Ankara Turkey

Harmonic generation is an attractive research field that finds a variety of application areas. However, harmonic generation within a medium of micron-scale interaction length limits the magnitude of nonlinear coupling and leads to poor harmonic generation efficiency. In this study, we present a constrained non-linear programming approach based on the Quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to obtain high-fidelity harmonic generation in optical micro-resonators. Using this approach, one can achieve high-intensity harmonic generation in a simple Fabry-Perot type optical micro-resonator. The generation of super-intense harmonics at a typical ultraviolet (UV)-ablation frequency of 820 THz and at pure yellow-light (515 THz) is investigated in particular. Moreover, we achieved more than 98% accuracy compared to well-known theoretical results. Our approach enables the design of highly efficient microscale harmonic generators to be used in integrated photonic devices.

关键词： harmonic generation non-linear wave mixing non-linear programming micro-resonator

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A tri-level approach for computing Stackelberg Markov game equilibrium: Computational analysis

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JOURNAL OF COMPUTATIONAL SCIENCE 2023年 68卷

作者： Clempner, Julio B. Inst Politecn Nacl Escuela Super Fiis & Matemat Bldg 9Ave Inst Politecn Nacl Mexico City 07738 DF Mexico Natl Polytech Inst Sch Phys & Math Mexico City DF Mexico

Tri-level game-theory problems have been drawing serious interest because of their applicability to a broad range of real applications. It is considered a hierarchical game (min-min-min) in which multiple leaders and followers compete restricted to finite, controllable and ergodic Markov games. We determine the relationship involving the Nash and Stackelberg equilibrium notions and typify the circumstances under which the proximal/gradient method converges to a Stackelberg equilibrium: the hierarchical structure considers that leaders and followers are in a Nash framework with a Stackelberg constraint model. Despite recent considerable progress, the literature to date has focused mostly on solutions based on linear programming. This paper introduces a new proximal/gradient method for computing the equilibrium point for a tri-level Stackelberg game played between multiple leaders and followers. This procedure guaranteed the convergence to a Stackelberg equilibrium. We also provide the analysis of the convergence and the rate of convergence to Stackelberg equilibrium point. Finally, we prove the effectiveness and utility of the proposed method using a numerical example.

关键词： Computational algorithm Tri-level game non-linear programming Stackelberg game Equilibrium Game theory Proximal gradient method

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Path Planning for Concentric Tube Robots: A Toolchain with Application to Stereotactic Neurosurgery

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IFAC-PapersOnLine 2023年第2期56卷 2871-2876页

作者： Matthias K. Hoffmann Willem Esterhuizen Karl Worthmann Kathrin Flaßkamp Systems Modeling and Simulation Systems Engineering Universität des Saarlandes Germany Optimization-based Control Group Institute of Mathematics Technische Universität Ilmenau Germany

We present a toolchain for solving path planning problems for concentric tube robots through obstacle fields. First, ellipsoidal sets representing the target area and obstacles are constructed from labelled point clouds. Then, the nonlinear and highly nonconvex optimal control problem is solved by introducing a homotopy on the obstacle positions where at one extreme of the parameter the obstacles are removed from the operating space, and at the other extreme they are located at their intended positions. We present a detailed example (with more than a thousand obstacles) from stereotactic neurosurgery with real-world data obtained from labelled MRI scans.

关键词： optimal control non-linear programming homotopy methods optimal path planning concentric tube robots stereotactic neurosurgery

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Systems Engineering Approach to the Optimization of Hot Blast Stoves

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IFAC Proceedings Volumes 1983年第15期16卷 47-54页

作者： K. Nose M. Takemura T. Morita Systems Control Research Section Asada Research Laboratory Kobe Steel Ltd. 53-3 Aza Maruyama Gomo Nada-Ku Kobe 657 Japan Energy Engineering Section Kobe Works Kobe Steel Ltd. 2 Higashi-machi Nadahama Nada-Ku Kobe 657 Japan

A systems engineering approach has been established to investigate the thermally efficient conditions of the hot blast stove system. A nonlinear optimization problem has been formulated. A mathematical model of the stove system with waste heat recovery equipments has been constructed. With this model, numerous constraints which are concerned with the hot blast supplied to the blast furnace and the stationary periodic operation of the stove system, have been provided. The performance index is the thermal efficiency of the stove system. In the non-linear optimization procedure, the GRG method has been adopted. The effects of the operating conditions and design variables of the stove system to the thermal efficiency have been investigated between 3-and 4-stove systems.

关键词： Steel industry hot blast stove system waste heat recovery energy control optimization non-linear programming

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Interval valued EOQ model with two types of defective items

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JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2018年第6期21卷 1059-1082页

作者： Ruidas, Subhendu Seikh, Mijanur Rahaman Nayak, Prasun Kumar Pal, Madhumangal Sonamukhi Coll Dept Math Bankura 722207 W Bengal India Kazi Nazrul Univ Dept Math Asansol 713340 W Bengal India Midnapore Coll Autonomous Dept Math Midnapore 721101 W Bengal India Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore 721102 W Bengal India

In the classical inventory model, the issue of quality of the product is not considered. It is assumed that all the items procured are of perfect quality. However, in real life production environment it is observed that some of the items produced are defective. Here, we have considered an Economic Order Quantity (EOQ) model with imperfect quality items where the incoming lot has fractions of scrap and re-workable items. These fractions are considered to be known with a certain given percentage. The demand from customers end is met with the perfect and re-worked items and the scrap items are sold differently at a salvage cost in a secondary market. Also to represent the real life situations, the inventory parameters have been taken as interval numbers. The corresponding mathematical problem has been formulated as an un-constrained optimization problem and has been solved using Particle Swarm Optimization (PSO) technique. Finally, the model has been illustrated with a numerical example.

关键词： Inventory Control Imperfect quality non-linear programming PSO technique

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New product introduction : determining optimal advertising policies

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Journal of Statistics and Management Systems 2004年第2期7卷 425-442页

The goodwill and time to introduce a new product in a market are the decision variables of a non-linear programming problem. Assuming an underlying goodwill dynamics derived from the Nerlove-Arrow’s model, we are faced with an objective function which is not differentiable over all the feasible set. After decomposing the problem into two differentiable non-linear programming problems we suggest a simple algorithm to solve it. A numerical analysis of the problems related with three different utility functions concludes the paper.

关键词： Marketing new product introduction non-linear programming

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Optimal Integration of Renewable Sources and Latent Heat Storages for Residential Application

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ENERGIES 2021年第17期14卷 5528页

作者： Manco, Giulia Guelpa, Elisa Verda, Vittorio Politecn Torino Energy Dept I-10129 Turin Italy

Given the large amount of energy required in the building sector, an interesting opportunity to reach future sustainable energy systems is the path towards low energy buildings. This work proposes an approach for optimally integrating building-scale energy technologies (both traditional and renewable) to enhance the transformation of the existing buildings (often energetically inefficient) in low-carbon systems. The approach promotes a transition sustainable from both the economic and environmental perspectives. Both operation and design optimization are considered with the aim of suggesting the best set of capacity of the technologies to be installed taking into account the expected operations. The building-scale technologies are integrated with proper storage units: Li-ion batteries and thermal storage (latent heat, that requires low installation space). As a dispatchable renewable technology, a biogas small-scale combined heat and power unit is included in the system. Once the key role played by this component in meeting the loads is proved, an analysis of the impact of the cost of the primary energy carrier of this technology on the system design is carried out. Two optimization approaches have been adopted (both based on non-linear programming). Results show that operation costs can be reduced by up to 29%. The adoption of a combined approach that takes into account both operation and design optimization lead to a reduction in installation and operating costs by up to 27%. In the analyzed cases, the use of the combined optimization confirms that latent heat storage is more suitable to be installed than electric storage (about -4.5% cost).

关键词： renewable technologies optimization non-linear programming latent heat storage small-scale wind turbine photovoltaic electric storage

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UAV Obstacle Avoidance Algorithm to Navigate in Dynamic Building Environments

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DRONES 2022年第1期6卷 16-16页

作者： Aldao, Enrique Gonzalez-deSantos, Luis M. Michinel, Humberto Gonzalez-Jorge, Higinio Univ Vigo Sch Aerosp Engn Engn Phys Grp Campus Ourense Orense 32004 Spain

In this work, a real-time collision avoidance algorithm was presented for autonomous navigation in the presence of fixed and moving obstacles in building environments. The current implementation is designed for autonomous navigation between waypoints of a predefined flight trajectory that would be performed by an UAV during tasks such as inspections or construction progress monitoring. It uses a simplified geometry generated from a point cloud of the scenario. In addition, it also employs information from 3D sensors to detect and position obstacles such as people or other UAVs, which are not registered in the original cloud. If an obstacle is detected, the algorithm estimates its motion and computes an evasion path considering the geometry of the environment. The method has been successfully tested in different scenarios, offering robust results in all avoidance maneuvers. Execution times were measured, demonstrating that the algorithm is computationally feasible to be implemented onboard an UAV.

关键词： UAVs in construction obstacle avoidance LiDAR optimization non-linear programming

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Can China Achieve the 2020 and 2030 Carbon Intensity Targets through Energy Structure Adjustment?

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ENERGIES 2018年第10期11卷 2721-2721页

作者： Wang, Ying Shang, Peipei He, Lichun Zhang, Yingchun Liu, Dandan Dongbei Univ Finance & Econ Sch Stat Dalian 116025 Peoples R China Dongbei Univ Finance & Econ Editorial Dept Dalian 116025 Peoples R China Dongbei Univ Finance & Econ Sch Publ Adm Dalian 116025 Peoples R China Qingdao Univ Sch Econ Qingdao 266071 Peoples R China

To mitigate global warming, the Chinese government has successively set carbon intensity targets for 2020 and 2030. Energy restructuring is critical for achieving these targets. In this paper, a combined forecasting model is utilized to predict primary energy consumption in China. Subsequently, the Markov model and non-linear programming model are used to forecast China's energy structure in 2020 and 2030 in three scenarios. Carbon intensities were forecasted by combining primary energy consumption, energy structure and economic forecasting. Finally, this paper analyzes the contribution potential of energy structure optimization in each scenario. Our main research conclusions are that in 2020, the optimal energy structure will enable China to achieve its carbon intensity target under the conditions of the unconstrained scenario, policy-constrained scenario and minimum external costs of carbon emissions scenario. Under the three scenarios, the carbon intensity will decrease by 42.39%, 43.74%, and 42.67%, respectively, relative to 2005 levels. However, in 2030, energy structure optimization cannot fully achieve China's carbon intensity target under any of the three scenarios. It is necessary to undertake other types of energy-saving emission reduction measures. Thus, our paper concludes with some policy suggestions to further mitigate China's carbon intensities.

关键词： carbon intensity target energy structure gray model (GM (1 1)) generalized regression neural network (GRNN) Markov forecasting model non-linear programming

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