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An interior point sequential quadratic programming-type method for log-determinant semi-infinite programs

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2020年 376卷 112784-000页

作者： Okuno, Takayuki Fukushima, Masao RIKEN Ctr Adv Intelligence Project AIP Chuo Ku Nihonbashi 1 Chome Mitsui Bldg15th Floor Tokyo 1030027 Japan Nanzan Univ Fac Sci & Engn Showa Ku 18 Yamazato Cho Nagoya Aichi 4668673 Japan

In this paper, we consider a nonlinear semi-infinite program that minimizes a function including a log-determinant (logdet) function over positive definite matrix constraints and infinitely many convex inequality constraints. We call this problem SIPLOG, where SIP stands for Semi-Infinite Program and LOG comes from LOG-det function. The main purpose of the paper is to develop an algorithm for efficiently computing a Karush-Kuhn-Tucker (KKT) point for the SIPLOG. More specifically, we propose an interior point sequential quadratic programming-type method that solves inexactly a sequence of semi-infinite quadratic programs approximating the SIPLOG. Furthermore, to generate a search direction in the dual matrix space associated with the semi-definite constraint, we solve scaled Newton equations that yield the family of Monteiro-Zhang directions. We prove that the proposed method weakly* converges to a KKT point under some mild assumptions. Finally, we conduct some numerical experiments to demonstrate the efficiency of the proposed method. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Semi-infinite program Log-determinant Interior point method sequential quadratic programming method Exchange method

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Quantitative analysis of neutron captured γ spectra using a sequential quadratic programming method

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JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 2014年 124卷 1-6页

作者： Wu, Wensheng Zhang, Lijuan Luo, Li China Univ Petr State Key Lab Petr Resources & Prospecting Beijing Peoples R China CNPC CCDC Well Logging Co Chongqing Peoples R China

High-precision, quantitative analysis is a key element in ensuring that neutron captured 7 spectral logging can be used to accurately distinguish rock minerals and rock types from complex reservoirs. We solve a nonlinear optimization problem by implementing a sequential quadratic programming method into a quantitative spectral analysis. To quantitatively test our method, we build three kinds of formation models with different porosities: a sandstone model, a mixed model of sandstone and limestone, and mixed model of sandstone, limestone, and ferric oxide. Combining results from Monte Carlo simulations, we analyze quantitatively the mixed spectra of the models using a sequential quadratic programming method and compare the results to those obtained with the weighted least-squares method. The results indicate that the sequential quadratic programming method can ensure high-precision, quantitative spectral analysis and that its spectral analysis precision is slightly higher than that of the weighted least-squares method. The sequential quadratic programming method has higher ability of adapting to complex lithology formation and can be used to analyze quantitatively the neutron gamma spectrum in complex lithology formations. (c) 2014 Elsevier B.V. All rights reserved.

关键词： geochemical logging quantitative analysis sequential quadratic programming method

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Shape Optimization for Arch Dam with sequential quadratic programming method

Shape Optimization for Arch Dam with Sequential Quadratic Pr...

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4th International Conference on Civil Engineering, Architecture and Building Materials (CEABM)

作者： Duan, Yin Yuan, Wei Liu, Huibo Changjiang Inst Survey Planning Design & Res Wuhan 430010 Peoples R China Wuhan Univ State Key Lab Water Res & Hydropower Engn Sci Wuhan 430072 Peoples R China

ISBN: (纸本)9783038351658

The sequential quadratic programming method is introduced in arch dam shape optimization design. In the optimization computation, the arch dam volume is taken as objective function, and the calculation is realized by automatically considering loading process, equivalent stress computation and simulation of shape optimization for arch dam based on FEM. A parabola arch dam is used as a numerical example. The result shows that the optimized figure is much safer and more practical, which indicates that the SQP method is an effective way for optimization design of arch dam shape.

关键词： Arch dam Optimization design FEM sequential quadratic programming method

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An equivalent nonlinear optimization model with triangular low-rank factorization for semidefinite programs

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OPTIMIZATION methodS & SOFTWARE 2023年第6期38卷 1296-1310页

作者： Yamakawa, Yuya Ikegami, Tetsuya Fukuda, Ellen H. H. Yamashita, Nobuo Kyoto Univ Grad Sch Informat Yoshida HonmachiSakyo Ku Kyoto 6068501 Japan Yahoo Japan Corp Data & Sci Solut Grp Technol Grp Chiyoda Ku Tokyo Japan

In this paper, we propose a new nonlinear optimization model to solve semidefinite optimization problems (SDPs), providing some properties related to local optimal solutions. The proposed model is based on another nonlinear optimization model given by [S. Burer and R. Monteiro, A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization, Math. Program. Ser. B 95 (2003), pp. 329-357], but it has several nice properties not seen in the existing one. Firstly, the decision variable of the proposed model is a triangular low-rank matrix. Secondly, the existence of a strict local optimum of the proposed model is guaranteed under some conditions, whereas the existing model has no strict local optimum. In other words, it is difficult to construct solution methods equipped with fast convergence using the existing model. We also present some numerical results, showing that the use of the proposed model allows to deliver highly accurate solutions.

关键词： Semidefinite optimization problems nonlinear optimization problems sequential quadratic programming method triangular low-rank factorization

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A global-local hybrid strategy with adaptive space reduction search method for structural health monitoring

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APPLIED MATHEMATICAL MODELLING 2023年第1期121卷 231-251页

作者： Zhang, Guangcai Wan, Chunfeng Xue, Songtao Xie, Liyu Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing Peoples R China Tongji Univ Res Inst Struct Engn & Disaster Reduct Coll Civil Engn Shanghai Peoples R China Tohoku Inst Technol Dept Architecture Sendai Japan

The difficulty in computational convergence poses challenges of application for traditional heuristic optimization algorithms to solve the optimization-based structural identification problem, especially for the large-scale and complex structural systems where considerable number of unknown parameters and degrees of freedom involved. Unlike the classic identification methods, in this paper, a novel hybrid strategy, coarsely exploring the relatively large search limits with the improved Jaya algorithm and adaptive search space reduction method in the global stage, and then fine-tuning the identified best solution with local optimization methods to the optimum in the local stage, is proposed and evaluated. The improved Jaya algorithm includes three improvements compared to its original version, fuzzy clustering competitive learning, experience learning and Cauchy mutation mechanisms. Gradient based Levenberg-Marquardt method, sequential quadratic programming method and non-gradient based Nelder-Mead simplex method are inserted as local mathematical optimizers to further enhance identification accuracy and efficiency. The superiority of proposed improved Jaya algorithm is validated in optimizing classical and CEC05 benchmark functions by comparing with several state-of-the-art algorithms. Furthermore, the effectiveness of proposed global-local hybrid method is verified by a numerical example of truss structure and an experimental test of the steel grid benchmark structure with incomplete set of noise-polluted measurements. The statistical results show that the improved Jaya algorithm and adaptive search space reduction method combined with sequential quadratic programming can achieve better performance in structural damage identification than other methods.

关键词： Structural identification Hybrid method Jaya algorithm Levenberg-marquardt method sequential quadratic programming method Nelder-mead simplex method

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Rotor blade aerodynamic shape optimization based on high-efficient optimization method

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 2020年第2期234卷 375-387页

作者： Wang, Qing Zhao, Qijun Lanzhou Univ Technol Coll Energy & Power Engn Lanzhou Gansu Peoples R China Nanjing Univ Aeronaut & Astronaut Natl Key Lab Sci & Technol Rotorcraft Aeromech Nanjing 210016 Jiangsu Peoples R China

In order to design a high-performance rotor, a high-efficient optimization method is established by coupling Kriging model and sequential quadratic programming with high-accuracy computational fluid dynamics method. In order to obtain the global optimal design point, the initial blade shape is optimized by using the Kriging model coupled with genetic algorithm based on the baseline rotor blade (Helishape 7A rotor). After that, the modified sequential quadratic programming method is employed to search the final blade shape based on the initial blade shape deeply. In the optimal process, the regions of design variables are restricted considering rotor dynamic characteristics. As a result, a new shape of rotor blade with characters of nonlinear twist, variational chord length, complex swept, and anhedral distributions is obtained. Compared with the baseline rotor, blade-tip vortex of the final optimized rotor is significantly weakened, the figure of merit of the final optimized rotor increases about 3.42%, and the peak of sound pressure decreases about 16.9%. At the same time, it is demonstrated that the final optimized rotor has better forward flight characteristics.

关键词： Helicopter rotor aerodynamic performance optimization sequential quadratic programming method N-S equations

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Optimal control of the power ramp rate with flicker mitigation for directly grid connected wind turbines

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SIMULATION-TRANSACTIONS OF THE SOCIETY FOR MODELING AND SIMULATION INTERNATIONAL 2020年第2期96卷 141-150页

作者： Jalalabadi, Esmaeil Salehizadeh, Mohammad Reza Kian, Ashkan Rahimi Univ Tehran Coll Engn Sch ECE SNLCIPCE Kargar St Tehran *** Iran Islamic Azad Univ Dept Elect Engn Marvdasht Branch Tehran Iran

In this paper, a detailed mathematical optimization model of electrolyzer/fuel cell technology connected to the grid through limited rating converters is developed. The model is so defined that it can tackle voltage fluctuation and meet the power ramp rate limitations inflicted by integration of constant-speed wind turbines at the Point of Common Coupling. The flicker mitigation and power ramp rate control problem in the presence of wind generation and variable electrical loads is defined as a nonlinear constrained optimization problem, in which voltage fluctuation is minimized as the objective function and the power ramp rate limitations are respected by the defined real-time ramp rate constraint. The problem is solved using the sequential quadratic programming method, which is a fast solver, by adjusting suitable initial points to be appropriate for real-time applications. The simulation results validate the efficiency of the proposed method and show dramatic improvement in flicker mitigation, power ramp rate control, and system rating reduction in comparison with the proportional-integral control method that was developed in previous studies.

关键词： Constant-speed wind turbine power ramp rate flicker mitigation optimal real-time control sequential quadratic programming method

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Effects of Van Der Waals Forces on the Vibration of Stacked Multilayered Graphene/Black Phosphorus Heterostructures

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INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS 2021年第8期21卷

作者： Hou, Dongchang Wang, Lifeng Zhang, Yiqing Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Nanjing 210016 Peoples R China

In this paper, the vibration of a stacked multilayered graphene/black phosphorus (G/BP) heterostructure is investigated via the mesh-free method. The shape function and its derivatives are addressed by the moving least squares (MLS) approach. Optimization of the sequential quadratic programming method is adopted to calculate the distance between the arbitrary layers. Therefore, coefficients of the van der Waals (vdW) interaction between arbitrary layers of heterostructures are obtained. Then the frequencies and mode shapes of the multilayered G/BP heterostructure, considering the vdW interaction between arbitrary layers, are compared with considering only the vdW interaction among adjacent layers. The effects of the number of layers and aspect ratio of the G/BP heterostructure on the frequencies are investigated. The results demonstrate that coefficients of the vdW interaction, considering the arbitrary layers, are larger than those considering only adjacent layers. The difference between natural frequencies considering arbitrary layers and those considering adjacent layers is not clear for the low-order cases. Alternatively, the difference between natural frequencies obtained considering arbitrary layers and those considering adjacent layers are obvious for high-order cases. This paper provides a useful method to optimize the vdW interaction between multilayered G/BP heterostructures and can adequately simulate their vibration behaviors.

关键词： sequential quadratic programming method mesh-free method vibration multilayered graphene black phosphorus heterostructures

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Energy-efficient QoS-based OCDMA networks aided by nonlinear programming methods

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AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS 2019年 98卷 144-155页

作者： Pendeza Martinez, Cristiane A. Durand, Fabio Renan Abrao, Taufik Univ Tecnol Fed Parana Campus Cornelio Procopio BR-86300000 Cornelio Procopio PR Brazil Univ Estadual Londrina Dept Elect Engn Rod Celso Garcia Cid PR445POB 10-011 BR-86057970 Londrina PR Brazil

One of the advantages of the optical code division multiple access (OCDMA) system networks over other multiple access methods is the ability to provide differentiated classes of quality of service (QoS) for different users. The performance of the OCDMA networks is mainly limited by the multi-access interference (MAI) coming from other users sharing the same spectral resources. The suitable resource allocation in OCDMA networks allows greater capacity and the reliable deployment of the available resources in the network. This work aiming at applying and analyzing four analytical optimization methods applied to energy efficiency (EE) maximization of OCDMA networks. Hence, such optimization methods were applied and their performance-complexity tradeoffs are compared, namely the augmented Lagrangian method (ALM) (Hadi and Pakravan, 2018), sequential quadratic programming method (SQP), majoration-minimization (MaMi) approach (Sun et al., 2017;Stoica, 2004), as well as Dinkelbach's method (DK). Tests were performed considering practical and realistic OCDMA networks with a wide range of nodes, typically K = {8;16: 32} nodes. The evaluated optimization methods were able to achieve convergence and perform suitably to solve the optical EE-OCDMA optimization problem. However, in a few specific high loading system configurations, the DK method did not reach full convergence;besides DK processing time was much greater compared to the promising ALM, SQP and MaMi EE-OCDMA optimization approaches. (C) 2018 Elsevier GmbH. All rights reserved.

关键词： Energy efficiency OCDMA networks Augmented Lagrangian method sequential quadratic programming method Majoration-minimization Dinkelbach's fractional optimization method CvX

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Novel repeatable launch locking/unlocking device for magnetically suspended momentum flywheel

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MECHATRONICS 2018年 54卷 16-25页

作者： Liu, Qiang Wang, Kun Ren, Yuan Peng Peilan Ma Limei Yin, Zhaojing Beijing Inst Petrochem Technol Inst Precis Electromagnet Equipment & Adv Measure Beijing Peoples R China Beihang Univ Key Lab Inertial Technol Beijing Peoples R China Space Engn Univ Sch Aerosp Sci & Technol Beijing Peoples R China

Because one-shot launch locking/unlocking device (OSLLUD) cannot repeat locking/unlocking, and repeatable launch locking/unlocking device (RLLUD) has an insufficient reliability of implementing unlocking, a novel RLLUD consisting of a motor, wire rope and several same flexible brackets was proposed. The composition, operating principle and functional performance requirements were introduced. A single flexible bracket was equivalent to a cantilever beam-mass model, and its static and dynamic performances were analyzed. Design variables were selected according to the sensitivity analysis method. Unlocking force, the maximum stress and the first resonance frequency were concerned, and the flexible brackets were optimized through the comparison and the sequential quadratic programming methods. The RLLUD was manufactured according to the optimization results. The environmental mechanics tests of tri-axial swept-sine and random vibration were carried out to verify the protective effect of the novel RLLUD for magnetically suspended momentum flywheel (MSMFW) during launch. The results show that the maximum macroscopic vibration is less than the protection gap of the flywheel, and its locking protective effect is valid and sufficient.

关键词： Magnetically suspended momentum flywheel Launch locking/unlocking device Optimization design sequential quadratic programming method Finite element method

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