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Solving the unit commitment problem of hydropower plants via Lagrangian Relaxation and sequential quadratic programming

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COMPUTATIONAL & APPLIED MATHEMATICS 2005年第3期24卷 317-341页

作者： Finardi, Erlon C. da Silva, Edson L. Sagastizabal, Claudia LabPlan Lab Planejamento Sistemas Energia Eletr BR-88040900 Florianopolis SC Brazil IMPA BR-22460320 Rio De Janeiro Brazil

We consider the optimal scheduling of hydropower plants in a hydrothermal interconnected system. This problem, of outmost importance for large-scale power systems with a high proportion of hydraulic generation, requires a detailed description of the so-called hydro unit production function. In our model, we relate the amount of generated hydropower to nonlinear tailrace levels;we also take into account hydraulic losses, turbine-generator efficiencies, as well as multiple 0-1 states associated with forbidden operation zones. Forbidden zones are crucial to avoid nasty phenomena such as mechanical vibrations in the turbine, cavitation, and low efficiency levels. The minimization of operating costs subject to such detailed constraints results in a large-scale mixed-integer nonlinear programming problem. By means of Lagrangian Relaxation, the original problem is split into a sequence of smaller and easy-to-solve subproblems, coordinated by a dual master program. In order to deal better with the combinatorial aspect introduced by the forbidden zones, we derive three different decomposition strategies, applicable to various configurations of hydro plants (with few or many units, which can be identical or different). We use a sequential quadratic programming algorithm to solve nonlinear subproblems. We assess our approach on a real-life hydroelectric configuration extracted from the south sub region of the Brazilian hydrothermal power system.

关键词： hydrothermal systems Unit Commitment Problems Lagrangian Relaxation sequential quadratic programming

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Posture Optimization in Robotic Flat-End Milling Based on sequential quadratic programming

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JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING-TRANSACTIONS OF THE ASME 2023年第6期145卷 061001-061001页

作者： Chen, Yongxue Ding, Ye State Key Lab Mech Syst & Vibrat Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ Sch Mech Engn Shanghai 200240 Peoples R China

Robotic flat-end milling of complex surfaces offers advantages such as high flexibility and high machining efficiency. In the process of planning the toolpath based on the cutter contact path, the robot functional redundancy and the tool orientation need to be solved carefully. This paper presents a posture optimization method for robotic flat-end milling. Taking the weighted sum of the machining width and the toolpath smoothness performance criterion as the objective function, an optimization model considering the joint limits and gouging avoidance is established. An efficient algorithm based on sequential quadratic programming is proposed to solve this nonconvex problem. During the execution of the algorithm, the machining width is efficiently calculated by an iterative method based on conformal geometric algebra, while its derivatives are approximated analytically. Simulations and experiments demonstrate that the presented technique can resolve the tool axis direction and the robot redundancy effectively to increase the machining width and improve the toolpath smoothness, thus reducing the time for machining and improving the surface quality.

关键词： robotic milling toolpath optimization sculptured surface flat-end cutter sequential quadratic programming CAD/CAM/CAE robotics and flexible tooling

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A sequential quadratic programming algorithm that combines merit function and filter ideas

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COMPUTATIONAL & APPLIED MATHEMATICS 2007年第3期26卷 337-379页

作者： Gomes, Francisco A. M. Univ Estadual Campinas Dept Appl Math IMECC BR-13081970 Campinas SP Brazil

A sequential quadratic programming algorithm for solving nonlinear programming problems is presented. The new feature of the algorithm is related to the definition of the merit function. Instead of using one penalty parameter per iteration and increasing it as the algorithm progresses, we suggest that a new point is to be accepted if it stays sufficiently below the piecewise linear function defined by some previous iterates on the (f, parallel to C parallel to(2)(2))-space. Therefore, the penalty parameter is allowed to decrease between successive iterations. Besides, one need not to decide how to update the penalty parameter. This approach resembles the filter method introduced by Fletcher and Leyffer [Math. Program., 91 (2001), pp. 239-269], but it is less tolerant since a merit function is still used. Numerical comparison with standard methods shows that this strategy is promising.

关键词： sequential quadratic programming merit functions filter methods

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Optimizing heat source distribution in sintering molds: Integrating response surface model with sequential quadratic programming

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HELIYON 2024年第8期10卷 e29376页

作者： Liu, Sanli Chen, Min Zhu, Nan Xiang, Zhouyi Huang, Songhua Zhang, Shunqi Xian Jiaotong Liverpool Univ Sch Adv Technol Suzhou Peoples R China ZINSIGHT Technol Shanghai Co Ltd Shanghai Peoples R China Shanghai Univ Sch Mechatron Engn & Automat Shanghai Peoples R China

The sintering mold imposes strict requirements for temperature uniformity. The mold geometric parameters and the power configuration of heating elements exert substantial influence. In this paper, we introduce an optimization approach that combines response surface models with the sequential quadratic programming algorithm to optimize the geometric parameters and heating power configuration of a heating system for sintering mold. The response surface models of the maximum temperature difference, maximum temperature, and minimum temperature of the sintering area are constructed utilizing the central composite design method. The model ' s reliability is rigorously confirmed through variance analysis, residual analysis, and generalization capability validation. The models demonstrate remarkable predictive accuracy within the design space. A nonlinear constrained optimization model is established based on the response surface models, and the optimal parameters are obtained after 9 iterations using the sequential quadratic programming algorithm. Under the optimal parameters, the maximum temperature difference is maintained at less than 5 degrees C, confirming exceptional temperature uniformity. We conduct parameter analysis based on standardized effects to determine the main influencing factors of temperature uniformity, revealing that the distance between adjacent heating rods and the power density of the inner heating rods exert significant influence. Enhanced temperature uniformity can be achieved by adopting a larger distance between heating rods and configuring the power density of the heating rods to a relatively modest level. This work introduces a practical approach to optimize the heating systems for sintering molds, with potential applications in various industrial mold optimization.

关键词： Temperature uniformity Sintering mold Response surface methodology sequential quadratic programming Optimal design

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Some new facts about sequential quadratic programming methods employing second derivatives

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OPTIMIZATION METHODS & SOFTWARE 2016年第6期31卷 1111-1131页

作者： Izmailov, A. F. Solodov, M. V. Lomonosov Moscow State Univ MSU Dept VMK Fac Uchebniy Korpus 2 Moscow 119991 Russia Peoples Friendship Univ Russia Miklukho Maklaya Str 6 Moscow 117198 Russia Derzhavin Tambov State Univ TSU Dept Math Phys & Comp Sci Int 33 Tambov 392000 Russia IMPA Inst Nacl Matemat Pura & Aplicada Estr Dona Castorina 110 BR-22460320 Rio De Janeiro Brazil

For the sequential quadratic programming method (SQP), we show that close to a solution satisfying the same assumptions that are required for its local quadratic convergence (namely uniqueness of the Lagrange multipliers and the second-order sufficient optimality condition), the direction given by the SQP subproblem using the Hessian of the Lagrangian is a descent direction for the standard l(1)-penalty function. We emphasize that this property is not straightforward at all, because the Hessian of the Lagrangian need not be positive definite under these assumptions or, in fact, under any other reasonable set of assumptions. In particular, this descent property was not known previously, under any assumptions (even including the stronger linear independence constraint qualification, strict complementarity, etc.). We also check the property in question by experiments on nonconvex problems from the Hock-Schittkowski test collection for a model algorithm. While to propose any new and complete SQP algorithm is not our goal here, our experiments confirm that the descent condition, and a model method based on it, work as expected. This indicates that the new theoretical findings that we report might be useful for full/practical SQP implementations which employ second derivatives and linesearch for the l(1)-penalty function. In particular, our results imply that in SQP methods where using subproblems without Hessian modifications is an option, this option has a solid theoretical justification at least on late iterations.

关键词： sequential quadratic programming penalty function descent direction quadratic convergence

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A progressive optimization for the inverse design of blade profile based on sequential quadratic programming

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE 2007年第1期221卷 23-31页

作者： Nan, X. Y. Liu, B. Jin, J. Northwestern Polytech Univ Sch Power & Energy Xian 710072 Shann Xi Peoples R China

In this paper, the potential-stream function method, a very efficient computational method for the inverse design of two-dimensional compressor blades in transonic flow conditions is presented. By investigating the influence of the prescribed velocity coefficient distribution on the blade surface, it is found that the non-physical solution usually obtained by the general inverse method could be effectively avoided by adjusting the local velocity coefficient distribution. The objective functions were set-up for the leading edge, trailing edge closing problems, and outlet flow angle, respectively, for the numerical optimization on the basis of sequential quadratic programming. The optimum blade profiles with satisfactory performance and reasonable geometric shape can be obtained by this improved optimization method.

关键词： profile shape leading edge trailing edge optimization sequential quadratic programming

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Integrated Intelligence of Fractional Neural Networks and sequential quadratic programming for Bagley-Torvik Systems Arising in Fluid Mechanics

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JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS 2020年第5期15卷 051003页

作者： Raja, Muhammad Asif Zahoor Manzar, Muhammad Anwaar Shah, Syed Muslim Chen, YangQuan COMSATS Univ Islamabad Dept Elect & Comp Engn Attock Campus Attock 43600 Pakistan Hamdard Univ Islamabad Hamdard Inst Engn & Technol Islamabad 44000 Pakistan Capital Univ Sci & Technol Dept Elect Engn Islamabad 44000 Pakistan Univ Calif Sch Engn 5200 North Lake Rd Merced CA 95343 USA

In this study, an efficient soft computing paradigm is presented for solving Bagley-Torvik systems of fractional order arising in fluid dynamic model for the motion of a rigid plate immersed in a Newtonian fluid using feed-forward fractional artificial neural networks (FrANNs) and sequential quadratic programming (SQP) algorithm. The strength of FrANNs has been utilized to construct an accurate modeling of the equation using approximation theory in mean square error sense. Training of weights of FrANNs is performed with SQP techniques. The designed scheme has been examined on different variants of the systems. The comparative studies of the proposed solutions with available exact as well as reference numerical results demonstrate the worth and effectiveness of the solver. The accuracy, consistency, and complexity are evaluated in depth through results of statistics.

关键词： Bagley-Torvik equation fractional differential equations neural networks artificial Intelligence sequential quadratic programming

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Co-design of a Continuously Variable Transmission using sequential quadratic programming-based Control Optimization

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IFAC-PapersOnLine 2020年第2期53卷 14350-14355页

作者： C.A. Fahdzyana M.C.F. Donkers T. Hofman Eindhoven University of Technology Netherlands

For systems with nonlinear dynamics, Dynamic programming for control is commonly considered in the framework of integrated plant and control system design. Despite its popularity, this control strategy can run into some computational issues as the performance is dependent on the state and input discretization. In this paper, we propose a sequential quadratic programming-based control optimization strategy for integrated system design, where both the plant and control are optimized for the case study of a continuously variable transmission. The proposed plant and control design problem will be solved using a nested strategy.

关键词： Multi-objective optimization optimization optimal control co-design sequential quadratic programming

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Separable Nonlinear Model Predictive Control via sequential quadratic programming for Large-scale Systems *

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IFAC-PapersOnLine 2015年第23期48卷 495-500页

作者： Liang Lu Department of Chemical and Biomolecular Engineering (BK21 Plus Program) Korea Advanced Institute of Science & Technology Daejeon Korea. Laboratory for Automatic Control and System Dynamics Technische Universität Chemnitz Chemnitz Germany.

In this paper, a sequential quadratic programming method is presented for largescale nonlinear and possibly non-convex model predictive control (MPC) optimization problem which is often set up with a separable objective function. By introducing the so-call consensus constraints to separate the couplings among the subsystems. The resulting QP subproblem is formulated in a separable form, which makes it possible to use the existing alternating direction methods, like ADMM, to efficiently compute Newton steps for the overall system in a distributed way. In order to enforce the convergence rate of the distributed computation, a distributed line search with local merit functions is also proposed.

关键词： sequential quadratic programming separable model predictive control alternating direction method of multipliers nonlinear systems non-convex optimization large-scale optimization distributed line search

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On the Application of sequential quadratic programming to State Constrained Optimal Control Problems

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IFAC Proceedings Volumes 1985年第2期18卷 31-39页

作者： J.L. de Jong K.C.P. Machielsen Department of Mathematics and Computing Science Eindhoven University of Technology Eindhoven. The Netherlands CAM-Centre CET. Philips Eindhoven. The Netherlands

In this paper a numerical method for the solution of state constrained optimal control problems is presented. The method is derived from an infinite dimensional analogue of sequential quadratic programming. The main purpose of the paper is to present some theoretical aspects of the method. An experimental numerical implementation of the method is discussed.

关键词： Numerical method state constrained optimal control sequential quadratic programming

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