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A sequential quadratic programming algorithm with an additional equality constrained phase

IMA JOURNAL OF NUMERICAL ANALYSIS 2012年第2期32卷 553-579页

作者： Luis Morales, Jose Nocedal, Jorge Wu, Yuchen Northwestern Univ Dept Elect Engn & Comp Sci Evanston IL 60208 USA Inst Tecnol Autonomo Mexico Dept Matemat Mexico City 01080 DF Mexico

A sequential quadratic programming (SQP) method is presented that aims to overcome some of the drawbacks of contemporary SQP methods. It avoids the difficulties associated with indefinite quadratic programming subproblems by defining this subproblem to be always convex. The novel feature of the approach is the addition of an equality constrained quadratic programming (EQP) phase that promotes fast convergence and improves performance in the presence of ill conditioning. This EQP phase uses exact second-order information and can be implemented using either a direct solve or an iterative method. The paper studies the global and local convergence properties of the new algorithm and presents a set of numerical experiments to illustrate its practical performance.

关键词： constrained optimization nonlinear programming sequential quadratic programming

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Formulating the optimization problem when using sequential quadratic programming applied to a simple LNG process

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COMPUTERS & CHEMICAL ENGINEERING 2015年 82卷 1-12页

作者： Wahl, Per E. Lovseth, Sigurd W. SINTEF Energy Res Gas Technol NO-7465 Trondheim Norway

sequential quadratic programming (SQP) may be very efficient compared with other techniques for the optimization of simple processes for the liquefaction of natural gas (LNG), and can be combined with process evaluation using commercial flowsheet simulators. However, the level of success is dependent on the formulation of the problem. In this work, effects of varying different aspects of the optimization problem formulation is investigated, such as variable selection, formulae for the estimation of derivatives, initial values, variable bounds, and formulation of constraints. Especially the formulation of the constraint for the temperature difference between the hot and cold composite curve is essential. The commonly used minimum temperature difference constraint should generally not be employed in gradient based optimization. Recommendations regarding optimization of simple LNG processes using SQP and flowsheet simulators are provided. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： LNG PRICO Optimization sequential quadratic programming Formulation of constraints

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Hybridization of Artificial Immune Systems and sequential quadratic programming for Dynamic Economic Dispatch

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2009年第9期37卷 1036-1045页

作者： Basu, M. Jadavpur Univ Dept Power Engn Kolkata 700098 India

Dynamic economic dispatch deals with the scheduling of online generator outputs with predicted load demands over a certain period of time so as to operate an electric power system most economically. This article proposes a hybrid methodology integrating artificial immune systems with sequential quadratic programming for solving the dynamic economic dispatch problem of generating units considering valve-point effects. This hybrid method incorporates artificial immune systems as a base level search, which can give good direction to the optimal region and sequential quadratic programming as a local search procedure, which is used to fine tune that region for achieving the final solution. Numerical results of a ten-unit system have been presented to demonstrate the performance and applicability of the proposed algorithm. The results obtained from the proposed algorithm are compared with those obtained from a hybrid of particle swarm optimization and sequential quadratic programming and a hybrid of evolutionary programming and sequential quadratic programming.

关键词： dynamic economic dispatch artificial immune systems sequential quadratic programming

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Hybrid imperialist competitive-sequential quadratic programming (HIC-SQP) algorithm for solving economic load dispatch with incorporating stochastic wind power: A comparative study on heuristic optimization techniques

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ENERGY CONVERSION AND MANAGEMENT 2014年 84卷 30-40页

作者： Morshed, Mohammad Javad Asgharpour, Alireza Univ Isfahan Esfahan Iran Shahid Chamran Univ Ahwaz Ahvaz Iran

The paper presents a new method based on a hybrid algorithm consisting of imperialist competitive algorithm (ICA) and sequential quadratic programming (SQP) technique to solve the power system economic load dispatch (ELD) problem. ICA could be taken into account as a powerful technique. Nevertheless, it may be trapped in local optima especially when numbers of imperialists increase. To alleviate this drawback, SQP is used to fine-tune the results of ICA to increase confidence in the solution. Renewable sources and wind energy especially have recently been getting more interest because of various environmental and economical considerations. So, wind power is included in the problem formulation. The incomplete gamma function (IGF) is used to characterize the impact of wind power. The hybrid imperialist competitive algorithm (ICA) and sequential quadratic programming (SQP) technique (HIC-SQP) is applied to solve economic load dispatch with incorporating stochastic wind power. To evaluate its effectiveness, the proposed method is tested on various power systems with 6, 13, 15, and 40 power plants with and without wind power. Simulation results of proposed method are compared with state-of-the-art heuristic optimization methods. It can be clearly seen that the proposed method improves the solution of ELD problem. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Imperialist competitive algorithm sequential quadratic programming Economic load dispatch Stochastic wind power Non-smooth cost functions

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FULLY STOCHASTIC TRUST-REGION sequential quadratic programming FOR EQUALITY-CONSTRAINED OPTIMIZATION PROBLEMS

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SIAM JOURNAL ON OPTIMIZATION 2024年第2期34卷 2007-2037页

作者： Fang, Yuchen Na, Sen Mahoney, Michael W. Kolar, Mladen Univ Chicago Comm Comp & Appl Math Chicago IL 60637 USA Univ Calif Berkeley Int Comp Sci Inst Berkeley CA 94720 USA Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA Univ Calif Berkeley Lawrence Berkeley Natl Lab Int Comp Sci Inst Berkeley CA 94720 USA Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA Univ Southern Calif Marshall Sch Business Los Angeles CA 90089 USA

We propose a trust-region stochastic sequential quadratic programming algorithm (TR-StoSQP) to solve nonlinear optimization problems with stochastic objectives and deterministic equality constraints. We consider a fully stochastic setting, where at each step a single sample is generated to estimate the objective gradient. The algorithm adaptively selects the trust-region radius and, compared to the existing line-search StoSQP schemes, allows us to utilize indefinite Hessian matrices (i.e., Hessians without modification) in SQP subproblems. As a trust-region method for constrained optimization, our algorithm must address an infeasibility issue---the linearized equality constraints and trust-region constraints may lead to infeasible SQP subproblems. In this regard, we propose an adaptive relaxation technique to compute the trial step, consisting of a normal step and a tangential step. To control the lengths of these two steps while ensuring a scale-invariant property, we adaptively decompose the trust-region radius into two segments, based on the proportions of the rescaled feasibility and optimality residuals to the rescaled full KKT residual. The normal step has a closed form, while the tangential step is obtained by solving a trust-region subproblem, to which a solution ensuring the Cauchy reduction is sufficient for our study. We establish a global almost sure convergence guarantee for TR-StoSQP and illustrate its empirical performance on both a subset of problems in the CUTEst test set and constrained logistic regression problems using data from the LIBSVM collection.

关键词： constrained stochastic optimization nonlinear optimization trust-region method sequential quadratic programming

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Constrained multiple indicator kriging using sequential quadratic programming

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COMPUTERS & GEOSCIENCES 2012年 48卷 211-219页

作者： Soltani-Mohammadi, Saeed Tercan, A. Erhan Univ Kashan Dept Min Engn Kashan Iran Hacettepe Univ Dept Min Engn Ankara Turkey

Multiple indicator kriging (MIK) is a nonparametric method used to estimate conditional cumulative distribution functions (CCDF). Indicator estimates produced by MIK may not satisfy the order relations of a valid CCDF which is ordered and bounded between 0 and 1. In this paper a new method has been presented that guarantees the order relations of the cumulative distribution functions estimated by multiple indicator kriging. The method is based on minimizing the sum of kriging variances for each cutoff under unbiasedness and order relations constraints and solving constrained indicator kriging system by sequential quadratic programming. A computer code is written in the Matlab environment to implement the developed algorithm and the method is applied to the thickness data. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： First and second kind of order relations Cumulative distribution function Negative kriging weights sequential quadratic programming Multiple indicator kriging

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Multi-material topology optimization for the transient heat conduction problem using a sequential quadratic programming algorithm

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ENGINEERING OPTIMIZATION 2018年第12期50卷 2091-2107页

作者： Long, Kai Wang, Xuan Gu, Xianguang North China Elect Power Univ Beijing Key Lab Energy Safety & Clean Utilizat Beijing Peoples R China North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewabl Beijing Peoples R China Changsha Univ Sci & Technol Educ Dept Hunan Prov Key Lab Safety Design & Reliabil Technol Engn Veh Changsha Hunan Peoples R China Dalian Univ Technol Dept Engn Mech State Key Lab Struct Anal Ind Equipment Dalian Peoples R China Hefei Univ Technol Sch Automobile & Traff Engn Hefei Anhui Peoples R China

Transient heat conduction analysis involves extensive computational cost. It becomes more serious for multi-material topology optimization, in which many design variables are involved and hundreds of iterations are usually required for convergence. This article aims to provide an efficient quadratic approximation for multi-material topology optimization of transient heat conduction problems. Reciprocal-type variables, instead of relative densities, are introduced as design variables. The sequential quadratic programming approach with explicit Hessians can be utilized as the optimizer for the computationally demanding optimization problem, by setting up a sequence of quadratic programs, in which the thermal compliance and weight can be explicitly approximated by the first and second order Taylor series expansion in terms of design variables. Numerical examples show clearly that the present approach can achieve better performance in terms of computational efficiency and iteration number than the solid isotropic material with penalization method solved by the commonly used method of moving asymptotes. In addition, a more lightweight design can be achieved by using multi-phase materials for the transient heat conductive problem, which demonstrates the necessity for multi-material topology optimization.

关键词： Transient heat conduction multi-material topology optimization thermal compliance sequential quadratic programming

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Design of a robust load frequency control using sequential quadratic programming technique

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2012年第1期40卷 1-8页

作者： Khodabakhshian, A. Pour, M. Ezatabadi Hooshmand, R. Univ Isfahan Dept Elect Engn Esfahan Iran

This paper presents a new methodology, named sequential quadratic programming (SQP), to design a robust PID controller for Load Frequency Control (LFC) of nonlinear interconnected power systems. This method easily copes with the nonlinear constraints such as Generation Rate Constraint (GRC) and it can be directly used on a nonlinear model of a multi-machine power system. The proposed controller is simple, effective and can ensure that the overall system performance is desirable. The robust performance of the proposed controller is compared with that of a conventional PI controller, and also with two other different techniques named PID-MPRS and PID-PSO through the simulation of two multi-machine power system examples with a variety of disturbances. Results show that the proposed technique gives a better performance. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Load frequency control Optimization Generation rate constraint sequential quadratic programming

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Backtracking search integrated with sequential quadratic programming for nonlinear active noise control systems

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APPLIED SOFT COMPUTING 2018年 73卷 666-683页

作者： Khan, Wasim Ullah Ye, ZhongFu Chaudhary, Naveed Ishtiaq Raja, Muhammad Asif Zahoor Univ Sci & Technol China Dept Elect Engn & Informat Sci Natl Engn Lab Speech & Language Informat Proc Hefei 230026 Anhui Peoples R China Int Islamic Univ Dept Elect Engn Islamabad Pakistan COMSATS Inst Informat Technol Dept Elect Engn Attock Pakistan

In the present work, integrated strength of backtracking search algorithm (BSA) and sequential quadratic programming (SQP) is exploited for nonlinear active noise control (ANC) systems. Legacy of approximation theory in mean squared sense is utilized to construct a cost function for ANC system based on finite impulse response (FIR) and Volterra filtering procedures. Global search efficacy of BSA aided with rapid local refinements with SQP is practiced for effective optimization of fitness function for ANC systems having sinusoidal, random and complex random signals under several variants based on linear/nonlinear and primary/secondary paths. Statistical observations demonstrated the worth of stochastic solvers BSA and BSA-SQP by means of accuracy, convergence and complexity indices. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Active noise control System identification Backtracking search algorithm sequential quadratic programming Hybrid computing

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Improved sequential quadratic programming Approach for Optimal Distribution Generation Deployments via Stability and Sensitivity Analyses

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2010年第14期38卷 1595-1614页

作者： Alhajri, M. F. Alrashidi, M. R. El-Hawary, M. E. Coll Technol Studies Dept Elect Engn PAAET Shuwaikh Kuwait Dalhousie Univ Dept Elect & Comp Engn Halifax NS Canada

Integrating distributed generation into an electric power system has an overall positive impact on the system. This impact can be enhanced via optimal distributed generation placement and sizing. In this article, the location issue is investigated through stability and sensitivity analyses. Distributed generation rating, on the other hand, is formulated as a non-linear optimization problem subject to high non-linear equality and inequality constraints. Sizing the distributed generation optimally is performed using a modified sequential quadratic programming method. The sequential quadratic programming is improved by incorporating the fast and flexible radial power flow routine, which was developed in an earlier work, to satisfy the power flow requirements. The proposed equality constraints satisfaction approach drastically reduces computational time requirements. This hybrid method is compared with conventional sequential quadratic programming, and the results are in favor of the proposed technique. The approach is designed to handle optimal single and multiple distributed generation placement and sizing with specified and unspecified power factors. A 69-bus distribution system is used to investigate the performance of the proposed approach.

关键词： distribution generation distributed generation optimal placement and sizing radial distribution power flow sequential quadratic programming stability and sensitivity indices

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