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A feasible trust-region sequential quadratic programming algorithm

SIAM JOURNAL ON OPTIMIZATION 2004年第4期14卷 1074-1105页

作者： Wright, SJ Tenny, MJ Univ Wisconsin Dept Comp Sci Madison WI 53706 USA Univ Wisconsin Dept Chem Engn Madison WI 53706 USA

An algorithm for smooth nonlinear constrained optimization problems is described, in which a sequence of feasible iterates is generated by solving a trust-region sequential quadratic programming (SQP) subproblem at each iteration and by perturbing the resulting step to retain feasibility of each iterate. By retaining feasibility, the algorithm avoids several complications of other trust-region SQP approaches: the objective function can be used as a merit function, and the SQP subproblems are feasible for all choices of the trust-region radius. Global convergence properties are analyzed under various assumptions on the approximate Hessian. Under additional assumptions, superlinear convergence to points satisfying second-order sufficient conditions is proved.

关键词： nonlinear constrained optimization feasible algorithm sequential quadratic programming trust-region algorithms

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Stabilized sequential quadratic programming

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 1999年第1-3期12卷 253-273页

作者： Hager, WW Univ Florida Dept Math Gainesville FL 32611 USA

Recently, Wright proposed a stabilized sequential quadratic programming algorithm for inequality constrained optimization. Assuming the Mangasarian-Fromovitz constraint qualification and the existence of a strictly positive multiplier (but possibly dependent constraint gradients), he proved a local quadratic convergence result. In this paper, we establish quadratic convergence in cases where both strict complementarity and the Mangasarian-Fromovitz constraint qualification do not hold. The constraints on the stabilization parameter are relaxed, and linear convergence is demonstrated when the parameter is kept fixed. We show that the analysis of this method can be carried out using recent results for the stability of variational problems.

关键词： sequential quadratic programming quadratic convergence superlinear convergence degenerate optimization stabilized SQP error estimation

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Nonlinear equality constraints in feasible sequential quadratic programming

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OPTIMIZATION METHODS & SOFTWARE 1996年第4期6卷 265-282页

作者： Lawrence, CT Tits, AL UNIV MARYLAND SYST RES INSTCOLLEGE PKMD 20742 UNIV MARYLAND DEPT ELECT ENGNCOLLEGE PKMD 20742

A simple scheme is proposed for handling nonlinear equality constraints in the context of a previously introduced sequential quadratic programming (SQP) algorithm for inequality constrained problems, generating iterates satisfying the constraints. The key is an idea due to Mayne and Polak (Math. Progr., vol. 11, pp. 67-80, 1976) by which nonlinear equality constraints are treated as ''less than or equal to''-type constraints to be satisfied by all iterates, thus precluding any positive value, and an exact penalty term is added to the objective function, thus penalizing negative values. Mayne and Polak obtained a suitable value of the penalty parameter by iterative adjustments based on a test involving estimates of the KKT multipliers. We argue that the SQP framework allows for a more effective estimation of these multipliers, and we provide convergence analysis of the resulting algorithm. Numerical results, obtained with the CFSQP code, are reported.

关键词： constrained optimization nonlinear equality constraints sequential quadratic programming feasibility

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Subspace-stabilized sequential quadratic programming

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2017年第1期67卷 129-154页

作者： Izmailov, A. F. Uskov, E. I. Lomonosov Moscow State Univ MSU VMK Fac OR Dept Uchebniy Korpus 2 Moscow 119991 Russia RUDN Univ Miklukho Maklaya Str 6 Moscow 117198 Russia Derzhavin Tambov State Univ Dept Math Phys & Comp Sci TSU Internationalnaya 33 Tambov 392000 Russia

The stabilized sequential quadratic programming (SQP) method has nice local convergence properties: it possesses local superlinear convergence under very mild assumptions not including any constraint qualifications. However, any attempts to globalize convergence of this method indispensably face some principal difficulties concerned with intrinsic deficiencies of the steps produced by it when relatively far from solutions;specifically, it has a tendency to produce long sequences of short steps before entering the region where its superlinear convergence shows up. In this paper, we propose a modification of the stabilized SQP method, possessing better "semi-local" behavior, and hence, more suitable for the development of practical realizations. The key features of the new method are identification of the so-called degeneracy subspace and dual stabilization along this subspace only;thus the name "subspace-stabilized SQP". We consider two versions of this method, their local convergence properties, as well as a practical procedure for approximation of the degeneracy subspace. Even though we do not consider here any specific algorithms with theoretically justified global convergence properties, subspace-stabilized SQP can be a relevant substitute for the stabilized SQP in such algorithms using the latter at the "local phase". Some numerical results demonstrate that stabilization along the degeneracy subspace is indeed crucially important for success of dual stabilization methods.

关键词： sequential quadratic programming Degenerate solution Noncritical Lagrange multiplier Dual stabilization Superlinear convergence Global convergence

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Design of Bio-inspired Heuristic Techniques Hybridized with sequential quadratic programming for Joint Parameters Estimation of Electromagnetic Plane Waves

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WIRELESS PERSONAL COMMUNICATIONS 2017年第1期96卷 1475-1494页

作者： Akbar, Sadiq Raja, Muhammad Asif Zahoor Zaman, Fawad Mehmood, Tariq Khan, Muhammd Abdul Rehman Univ Peshawar Dept Elect Peshawar Pakistan COMSATS Inst Informat Technol Dept Elect Engn Attock Campus Attock Pakistan

In this study, intelligent hybrid computing techniques are developed using variants of genetic algorithms (GAs) to estimate jointly direction of arrival and amplitude of electromagnetic plane waves. Fitness evaluation function is formulated for parameter estimation model by exploiting the approximation theory in mean square sense based on error between the desired and estimated responses. Optimization of design variables of the model is carried out with hybrid schemes through variant of GAs integrated with sequential quadratic programming for rapid refinement. Proposed schemes are applied to number of electromagnetic plane waves impinging on uniform linear array from different directions with different amplitudes. Comparison of the results is done with true parameters of the system in order to evaluate the performance of the algorithms. Monte-Carlo simulations for the design approaches are carried out to analyze their strength in terms of estimation accuracy, robustness against noise, convergence and proximity effects.

关键词： Direction of arrival Genetic algorithms Memetic computing sequential quadratic programming Parameters estimations

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Design of artificial neural network models optimized with sequential quadratic programming to study the dynamics of nonlinear Troesch's problem arising in plasma physics

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NEURAL COMPUTING & APPLICATIONS 2018年第6期29卷 83-109页

作者： Raja, Muhammad Asif Zahoor Shah, Fiaz Hussain Tariq, Muhammad Ahmad, Iftikhar Ahmad, Siraj ul Islam COMSATS Inst Informat Technol Dept Elect Engn Attock Campus Attock Pakistan RIPHAH Int Univ Dept Basic Sci Islamabad Pakistan Univ Gujrat Dept Math Gujrat Pakistan COMSATS Inst Informat Technol Dept Phys Islamabad Pakistan

In this study, a computational intelligence technique based on three different designs of artificial neural networks (ANNs) is presented to solve the nonlinear Troesch's boundary value problem arising in plasma physics. The structure of three ANN models is formulated by incorporating log-sigmoid (ANN-LS), radial-base (ANN-RB) and tan-sigmoid (ANN-TS) kernel functions in the hidden layers. Mathematical modeling of the problem is constructed for all three feed-forward ANN models by defining an error function in an unsupervised manner. sequential quadratic programming method is employed for the learning of unknown parameters for all three ANN-LS, ANN-RB and ANN-TS schemes. The proposed models are applied to solve variants of Troesch's problems by taking the small and large values of critical parameter in the system. A comparison of the proposed solution obtained from these models has been made with the standard numerical results of Adams method. The accuracy and convergence of the proposed models are investigated through results of statistical analysis in terms of performance indices based on the mean absolute deviation, root-mean-square error and variance account for.

关键词： Artificial neural networks sequential quadratic programming Troesch's problem Stochastic solvers Activation functions

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Profile error evaluation of free-form surface using sequential quadratic programming algorithm

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PRECISION ENGINEERING-JOURNAL OF THE INTERNATIONAL SOCIETIES FOR PRECISION ENGINEERING AND NANOTECHNOLOGY 2017年 47卷 344-352页

作者： Lang, Ailei Song, Zhanjie He, Gaiyun Sang, Yicun Tianjin Univ Sch Sci Tianjin 300350 Peoples R China Tianjin Univ Minist Educ Key Lab Mech Theory & Equipment Design Tianjin 300350 Peoples R China

Profile error of free-form surface is evaluated in this paper based on sequential quadratic programming (SQP) algorithm. The optimal localization model is established with the minimum zone criterion firstly. Subsequently, the surface subdivision method or STL (STeror Lithography) model is used to compute the point-to-surface distance and the approximate linear differential movement model of signed distance is deduced to simplify the updating process of alignment parameters. Finally, the optimization model on profile error evaluation of free-form surface is solved with SQP algorithm. Simulation examples indicate that the results acquired by SQP method are closer to the ideal results than the other algorithms in the problem of solving transformation parameters. In addition, real part experiments show that the maximum distance between the measurement points and their corresponding closest points on the design model is shorter by using SQP-based algorithm. Lastly, the results obtained in the experiment of the workpiece with S form illustrate that the SQP-based profile error evaluation algorithm can dramatically reduce the iterations and keep the precision of result simultaneously. Furthermore, a simulation is conducted to test the robustness of the proposed method. In a word, this study purposes a new algorithm which is of high accuracy and less time-consuming. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Free-form surface profile error Signed distance function Surface subdivision STL model sequential quadratic programming

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Using a Filter-Based sequential quadratic programming Algorithm in a Parallel Environment

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JOURNAL OF AEROSPACE COMPUTING INFORMATION AND COMMUNICATION 2009年第12期6卷 635-648页

作者： Venter, Gerhard Vanderplaats, Garret N. Univ Stellenbosch Dept Mech & Mech Engn ZA-7602 Stellenbosch South Africa Vanderplaats Res & Dev Inc Monterey CA 93940 USA

A parallel, filter-based, sequential quadratic programming algorithm is implemented and tested for typical general-purpose engineering applications. Constrained engineering test problems, including a finite element simulation, with up to 512 design variables are considered. The accuracy and serial performance of the filter-based algorithm are compared against that of a standard sequential quadratic programming algorithm. The parallel performance of the algorithm is evaluated, using up to 52 cores on a Linux Cluster. The results indicate that the filter-based algorithm competes favorably with a standard sequential quadratic programming algorithm in a serial environment. However, the filter-based algorithm exhibits much better parallel efficiency due to the lack of a one-dimensional search.

关键词： sequential quadratic programming Parallel Computing Finite Element Analysis sequential Linear programming High Performance Computing Particle Swarm Optimization Nonlinear programming Numerical Simulation Parallel Algorithm Young's Modulus

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Consensus fuzzy clustering by sequential quadratic programming approach

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2023年第2期44卷 1847-1863页

作者： Samimi, Navid Nejatian, Samad Parvin, Hamid Bagherifard, Karamollah Rezaei, Vahideh Islamic Azad Univ Dept Comp Engn Yasooj Branch Yasuj Iran Islamic Azad Univ Dept Elect Engn Yasooj Branch Yasuj Iran Islamic Azad Univ Dept Comp Engn Nourabad Mamasani Branch Nourabad Mamasani Iran Islamic Azad Univ Dept Math Yasooj Branch Yasuj Iran

Existing fuzzy clustering ensemble approaches do not consider dependability. This causes those methods to be fragile in dealing with unsuitable basic partitions. While many ensemble clustering approaches are recently introduced for improvement of the quality of the partitioning, but lack of a median partition based consensus function that considers more participate reliable clusters, remains unsolved problem. Dealing with the mentioned problem, an innovative weighting fuzzy cluster ensemble framework is proposed according to cluster dependability approximation. For combining the fuzzy clusters, a fuzzy co-association matrix is extracted in a weighted manner out of initial fuzzy clusters according to their dependabilities. The suggested objective function is a constrained nonlinear objective function and we solve it by sparse sequential quadratic programming (SSQP). Experimentations indicate our method can outperform modern clustering ensemble approaches.

关键词： Fuzzy cluster ensemble cluster dependability consensus function base clustering sequential quadratic programming

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Some composite-step constrained optimization methods interpreted via the perturbed sequential quadratic programming framework

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OPTIMIZATION METHODS & SOFTWARE 2015年第3期30卷 461-477页

作者： Izmailov, A. F. Kurennoy, A. S. Solodov, M. V. Moscow MV Lomonosov State Univ OR Dept VMK Fac Moscow 119991 Russia IMPA BR-22460320 Rio De Janeiro RJ Brazil

We consider the inexact restoration and the composite-step sequential quadratic programming (SQP) methods, and relate them to the so-called perturbed SQP framework. In particular, iterations of the methods in question are interpreted as certain structured perturbations of the basic SQP iterations. This gives a different insight into local behaviour of those algorithms, as well as improved or different local convergence and rate of convergence results.

关键词： sequential quadratic programming inexact restoration perturbed SQP composite-step SQP superlinear convergence

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