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Computational experience with a safeguarded barrier algorithm for sparse nonlinear programming

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2001年第1期19卷 107-120页

作者： Gajulapalli, RS Lasdon, LS Univ Texas Coll Business Adm MSIS Dept Austin TX 78712 USA

We describe an enhanced version of the primal-dual interior point algorithm in Lasdon, Plummer, and Yu (ORSA Journal on Computing, vol. 7, no. 3, pp. 321-332, 1995), designed to improve convergence with minimal loss of efficiency, and designed to solve large sparse nonlinear problems which may not be convex. New features include (a) a backtracking linesearch using an L1 exact penalty function, (b) ensuring that search directions are downhill for this function by increasing Lagrangian Hessian diagonal elements when necessary, (c) a quasi-Newton option, where the Lagrangian Hessian is replaced by a positive definite approximation (d) inexact solution of each barrier subproblem, in order to approach the central trajectory as the barrier parameter approaches zero, and (e) solution of the symmetric indefinite linear Newton equations using a multifrontal sparse Gaussian elimination procedure, as implemented in the MA47 subroutine from the Harwell Library (Rutherford Appleton Laboratory Report RAL-95-001, Oxfordshire, UK, Jan. 1995). Second derivatives of all problem functions are required when the true Hessian option is used. A Fortran implementation is briefly described. Computational results are presented for 34 smaller models coded in Fortran, where first and second derivatives are approximated by differencing, and for 89 larger GAMS models, where analytic first derivatives are available and finite differencing is used for second partials. The GAMS results are, to our knowledge, the first to show the performance of this promising class of algorithms on large sparse NLP's. For both small and large problems, both true Hessian and quasi- Newton options are quite reliable and converge rapidly. Using the true Hessian, INTOPT is as reliable as MINOS on the GAMS models, although not as reliable as CONOPT. Computation times are considerably longer than for the other 2 solvers. However, interior point methods should be considerably faster than they are here when analytic second

关键词： non linear programming barrier algorithm sqp algorithm large sparse problems

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A smoothing trust-region Newton-CG method for minimax problem

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APPLIED MATHEMATICS AND COMPUTATION 2008年第2期199卷 581-589页

作者： Ye, Feng Liu, Hongwei Zhou, Shuisheng Liu, Sanyang Xidian Univ Sch Sci Dept Appl Math Xian 710071 Peoples R China

This paper presents a smooth approximate method with a new smoothing technique and a standard unconstrained minimization algorithm in the solution to the finite minimax problems. The new smooth approximations only replace the original problem in some neighborhoods of the kink points with a twice continuously differentiable function, its gradient and Hessian matrix are the combination of the first and the second order derivative of the original functions respectively. Compared to the other smooth functions such as the exponential penalty function, the remarkable advantage of the new smooth function is that the combination coefficients of its gradient and the Hessian matrix have sparse properties furthermore, the maximal possible difference value between the optimal values of the smooth approximate problem and the original one is determined by a fixed parameter selected previous. An algorithm to solve the equivalent unconstrained problem by using the trust-region Newton conjugate gradient method is proposed in the solution process finally, some numerical examples are reported to compare the proposed algorithm with sqp algorithm that implements in MATLAB toolbox and the algorithm in [E. Polak, J. O. Royset, R. S. Womersley, algorithms with adaptive smoothing for finite minimax problems, Journal of Optimization Theory and Applications 119 (3) (2003) 459-484] based on the exponential penalty function, the numerical results prove that the proved algorithm is efficient. (c) 2008 Elsevier Inc. All rights reserved.

关键词： finite minimax problem smooth technique unconstrained optimization sqp algorithm trust-region Newton-CG algorithm

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A dynamic optimization method for power distribution network operation with high ratio photovoltaics

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IET GENERATION TRANSMISSION & DISTRIBUTION 2022年第21期16卷 4417-4432页

作者： Liu, Keyan Zhan, Huiyu Wei, Yuhan Kang, Tianyuan China Elect Power Res Inst 15 Xiaoying E Rd Beijing 100192 Peoples R China

With the high ratio distributed photovoltaics (PVs) penetration to the distribution network (DN), the bearing capacity, integration capacity, consuming capacity and controlling capacity of DN for PVs are all facing great challenges. Enhancing the flexible regulation and operation optimization capabilities of DN have become key factors to satisfy these new challenges. For the operation optimization problem of high ratio PVs penetration, a novel quasi-equal curtailment ratio (QCR) constraint of PVs is proposed in the dynamic optimization method for DN operation. Firstly, the uncertainty of high ratio PVs and their active power deviations are discussed. And a dynamic optimization framework of PVs based on optimal power flow (OPF) has been proposed. Secondly, the optimization model for high ratio PVs is formulated with multi-objective of maximum PVs output, minimum voltage deviation and minimum line loss, under the equality and inequality constraints of power flow, PVs power generation limit, QCR of PVs and so on. Then the multi-objective optimization problem (MOP) is transformed into a single-objective optimization problem (SOP) by weighting coefficients, and solved by sequential quadratic programming (sqp) with trust-region (TR) searching algorithm. Finally, the proposed method is tested, verified and compared with the primal dual interior point (PDIP) and traditional sqp algorithms in IEEE 33-bus, PG&E 69-bus, 292-bus and 1180-bus test cases. The experimental results show the rapidity and robustness of the proposed method.

关键词： search problems PV power generation limit operation optimization problem optimal power flow sqp algorithm high ratio distributed photovoltaic penetration quadratic programming QCR multiobjective optimization problem single-objective optimization problem dynamic optimization framework minimum line loss primal dual interior point dynamic optimization method active power deviation bearing capacity trust-region searching algorithm controlling capacity photovoltaic power systems high ratio PVs penetration power generation economics IEEE 292-bus test case power distribution network operation IEEE 33-bus test case minimum voltage deviation distributed power generation PG&E 69-bus test case IEEE 1180-bus test case novel quasiequal curtailment ratio constraint optimization model sequential quadratic programming integration capacity consuming capacity load flow demand side management flexible regulation DN operation power distribution economics PDIP

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A superlinearly convergent numerical algorithm for nonlinear programming

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NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 2012年第5期13卷 2391-2402页

作者： Zhu, Zhibin Wang, Shuo Guilin Univ Elect Technol Coll Math & Comp Sci Guilin 541004 Peoples R China

In this paper, a new algorithm is proposed to solve the nonlinear constrained optimization problems. Unlike sequential quadratic programming (sqp) type methods, this algorithm does not involve solutions of quadratic programs. It is merely necessary to solve systems of linear equations with small scale to obtain a direction. The scheme is based on an idea of E-effective active set strategies. The theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Inequality constrained optimization sqp algorithm QP-free algorithm Global convergence Super linear convergence rate

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Optimal operation strategy development for fuel cell hybrid vehicle

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JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY 2011年第1期25卷 183-192页

作者： Xuan, D. J. Kim, J. W. Kim, Y. B. Chonnam Natl Univ Dept Mech Engn Kwangju South Korea Wenzhou Univ Coll Mech Engn Wenzhou Peoples R China Adv Mechatron Syst Co Res Ctr Kwangju South Korea

An overall simulation model for fuel cell hybrid vehicle (FCHV) power train in parallel configuration using MATLAB/Simulink programming is constructed in this study. The model runs on power control strategy by using logic-threshold approach, achieved by the hybrid control unit (HCU) and fuel cell stack number. Using accelerator and decelerator pedal positions deduced from the driving schedule as the primary input, the simulation implements power flow and distribution under different vehicle operating modes. The HCU control strategy also incorporates regenerative braking and recharge for battery capacity recovery. Using the D-optimality method for experiment points selection and sequential quadratic programming (sqp) algorithm for obtaining the optimal operational parameters, three control threshold variables of HCU and optimal stack cell number are selected for hydrogen fuel economy under certain driving cycles. The proposed method provides optimized configurations of the FCHV model and the fuel cell stack, which has the capability in satisfying drive power request while satisfying vehicle driving schedule and battery state of charge (SOC) recovery with lower fuel consumption.

关键词： FCHV HCU Modeling Logic threshold D-optimality sqp algorithm

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Efficiency Optimization of IPOP DC/DC System for HEV

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IEEE ACCESS 2021年 9卷 31553-31561页

作者： Lu, Fengwang He, Liangzong Tan, Qingyang Zhou, Hongyan Xiamen Univ Sch Aeronaut & Astronaut Xiamen 361000 Peoples R China

Input parallel output parallel (IPOP) DC/DC system is widely utilized in many occasions like data center and hybrid electric vehicle (HEV). However, the efficiency characteristics of different converters usually differs from each other, and the conventional control strategy has difficult to realize efficient conversion of overall power of the system. To address this issue, Buck converter is taken as the module and whose efficiency model under current continuous conduction mode (CCM) is presented. Meantime, parameter identification method based on least square (LS) algorithm is proposed as well. In order to realize the efficiency optimization of the whole parallel system, the constraint conditions of each module are analyzed, and the current distribution calculation method based on sequential quadratic programming (sqp) algorithm for the parallel system is introduced. On this basis, a control strategy of proportional current distribution (PCD) is proposed, which not only ensures that the parallel system can always run as efficiently as possible under different loads, but also realizes the flexible switching between the current-sharing mode and current distribution mode. Finally, the simulation and experimental results prove that the proposed method can achieve 4.46% higher efficiency than conventional method within the given power range of each converter, and realize the efficiency optimization of the IPOP DC/DC system to the greatest extent.

关键词： Optimization Current distribution Hybrid electric vehicles Power distribution Mathematical model Buck converters Parameter estimation Efficiency optimization LS algorithm proportional current distribution IPOP DC DC converter sqp algorithm

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Computational finite element model updating tool for modal testing of structures

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STRUCTURAL ENGINEERING AND MECHANICS 2014年第2期51卷 229-248页

作者： Sahin, Abdurrahman Bayraktar, Alemdar Yildiz Tekn Univ TR-34220 Istanbul Turkey Karadeniz Tech Univ TR-61080 Trabzon Turkey

In this paper, the development of a new optimization software for finite element model updating of engineering structures titled as FemUP is described. The program is used for computational FEM model updating of structures depending on modal testing results. This paper deals with the FE model updating procedure carried out in FemUP. The theoretical exposition on FE model updating and optimization techniques is presented. The related issues including the objective function, constraint function, different residuals and possible parameters for FE model updating are investigated. The issues of updating process adopted in FemUP are discussed. The ideas of optimization to be used in FE model updating application are explained. The algorithm of Sequential Quadratic Programming (sqp) is explored which will be used to solve the optimization problem. The possibilities of the program are demonstrated with a three dimensional steel frame model. As a result of this study, it can be said that sqp algorithm is very effective in model updating procedure.

关键词： finite element model updating optimization experimental modal analysis operational modal analysis SignalCAD ModalCAD FemUP MATLAB sqp algorithm

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An efficient sequential quadratic programming algorithm for nonlinear programming

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2005年第2期175卷 447-464页

作者： Zhu, ZB Guilin Inst Elect Technol Dept Computat Sci & Math Guilin 541004 Peoples R China

In this paper, a new feasible sequential quadratic programming (Fsqp) algorithm is proposed to solve the nonlinear programming, where a feasible descent direction is obtained by solving only one QP subproblem. In order to avoid Maratos effect, a high-order revised direction is computed by solving a linear system with involving some "active" constraints. The theoretical analysis shows that global and superlinear convergence can be deduced. (C) 2004 Elsevier B.V. All rights reserved.

关键词： inequality constrained optimization method of feasible direction sqp algorithm global convergence superlinear convergence rate

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Deriving coordinated experts' weights based on sequential quadratic programming algorithm for multi-attribute group decision making

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SOFT COMPUTING 2023年第8期27卷 4865-4878页

作者： He, Jianqing Yang, Yanxia Guangdong Ocean Univ Fac Math & Comp Sci Zhanjiang 524088 Peoples R China Guangdong Ocean Univ Fac Elect & Informat Engn Zhanjiang 524088 Peoples R China

When evaluating the closeness between the decision matrix given by each expert and the overall decision matrix, we should pay more attention to the consistency of the ranking of candidates rather than the deviation degree of the scoring size. Therefore, in this paper, the modified cosine distance measure, instead of the Euclidean distance measure, is used to calculate the proximity between each expert decision matrix and the overall decision matrix. Furthermore, in order to receive more reasonable weights of experts, a new definition of coordinated expert weights in an optimization way is proposed. And then, the sequential quadratic programming (sqp) algorithm is used to derive the coordinated weights of experts, which is not affected by the selection of the initial value of expert weights and can objectively reflect the scoring level of each expert. Since different sorting methods would have inconsistent sorting results, a combined method based on sqp algorithm to derive the coordinated weights of different sorting methods is proposed to promote the ability of ranking the alternatives. Finally, numerical experiments are used to demonstrate the effectiveness of the sqp algorithm to derive coordinated expert weights with the modified cosine distance measure and the superiority of the combined method to rank alternatives.

关键词： Group decision-making Coordinated weights of experts sqp algorithm Combined method

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A systematic simulation and optimization of an industrial-scale p-xylene simulated moving bed process

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SEPARATION AND PURIFICATION TECHNOLOGY 2018年 191卷 48-60页

作者： Shen, Yuanhui Fu, Qiang Zhang, Donghui Na, Ping Tianjin Univ Sch Chem Engn & Technol Collaborat Innovat Ctr Chem Sci & Engn State Key Lab Chem EngnRes Ctr Chem Engn Tianjin 300072 Peoples R China

This work presents a detailed study for the systematic analysis, simulation and optimization of an industrial-scale simulated moving bed process with Ba/K-exchanged faujasite-type zeolite as adsorbent for separating p-xylene from the C-8 aromatic mixture. The adsorption equilibrium of C-8 aromatic isomers and p-diethylbenzene on the commercial adsorbent were determined experimentally, while the lumped mass transfer coefficients were estimated through pulse experimental results. A generic mathematic model incorporating the fixed model, node model as well as dead volume model was developed to implement a numerical simulation of an industrial-scale p-xylene simulated moving bed process. Moreover, the accuracy of mathematic model was validated by industrial data. Furthermore, a dynamic optimization framework, with state of the art Sequential Quadratic programming optimization algorithm, was firstly proposed to obtain the optimal operating conditions for an existing industrial simulated moving bed unit. Optimization results reflect that the desorbent consumption of p-diethylbenzene was favorable to be selected as objective function to be minimized, which could achieve 3.12% increase in SMB unit productivity and 8.66% decrease in desorbent consumption for seven zone p-xylene simulated moving bed process. Two-level optimization procedure was also constructed to get the maximum feed throughput with a desired minimized desorbent consumption. Under the optimal operating conditions, the productivity increases by 16.63% while the PDEB consumption decreases by 18.85% for seven zone p-xylene simulated moving bed process. Eight zone p-xylene simulated moving bed process as a new operating mode, which was also analyzed, emulated and optimized through numerical calculation. Results show that the eight zone operation could achieve a much higher productivity and the desorbent consumption of p-diethylbenzene was almost the same in comparison with seven zone operation.

关键词： para-Xylene Simulated moving bed Modeling Optimization sqp algorithm

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