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A semismooth sequential quadratic programming method for lifted mathematical programs with vanishing constraints

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2011年第6期51卷 919-941页

作者： Izmailov, A. F. Pogosyan, A. L. Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Moscow 119991 Russia

Mathematical programs with vanishing constraints are a difficult class of optimization problems with important applications to optimal topology design problems of mechanical structures. Recently, they have attracted increasingly more attention of experts. The basic difficulty in the analysis and numerical solution of such problems is that their constraints are usually nonregular at the solution. In this paper, a new approach to the numerical solution of these problems is proposed. It is based on their reduction to the so-called lifted mathematical programs with conventional equality and inequality constraints. Special versions of the sequential quadratic programming method are proposed for solving lifted problems. Preliminary numerical results indicate the competitiveness of this approach.

关键词： mathematical program with vanishing constraints lifted problem mathematical program with complementarity constraints constraint qualifications optimality conditions sequential quadratic programming

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A sequential quadratic programming algorithm without a penalty function, a filter or a constraint qualification for inequality constrained optimization

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OPTIMIZATION 2022年第6期71卷 1603-1635页

作者： Jian, Jinbao Tang, Chunming Hu, Qingjie Han, Daolan Guangxi Univ Nationalities Coll Math & Phys Guangxi Key Lab Hybrid Computat & IC Design Anal Ctr Appl Math & Artificial Intelligence Nanning Peoples R China Guangxi Univ Coll Math & Informat Sci Nanning Peoples R China Guilin Univ Elect & Technol Sch Math & Computat Sci Guilin Peoples R China

This paper discusses a kind of nonlinear inequality constrained optimization problems without any constraint qualification. A new sequential quadratic programming algorithm for such problems is proposed, whose important features are as follows: (i) a new relaxation technique for the linearized constraints of the quadratic programming subproblem is introduced, which guarantees that the subproblem is always consistent and generates a favourable search direction;(ii) a weaker positive-definiteness assumption on the quadratic coefficient matrices is presented;(iii) a slightly new line search is adopted, where neither a penalty function nor a filter is used;(iv) an associated acceptable termination rule is introduced;(v) the finite convergence of the algorithm is proved. Furthermore, the numerical results on a collection of CUTE test problems show that the proposed algorithm is promising.

关键词： Inequality constraints nonlinear programming sequential quadratic programming line search finite convergence

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An effective nonlinear interval sequential quadratic programming method for uncertain inverse problems

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STRUCTURES 2023年 51卷 615-627页

作者： Tang, Jiachang Lei, Yong Zhang, Taolin Yao, Qishui Fu, Chunming Zhan, Lina Mi, Chengji Hunan Univ Technol Dept Mech Engn Zhuzhou 412007 Peoples R China Univ South China Coll Mech Engn Hengyang 421001 Peoples R China

An effective nonlinear interval sequential quadratic programming method is proposed to provide an efficient tool for uncertain inverse problems. Assisted by the ideology of sequential quadratic programming and dimension -reduction analysis theory, the interval inverse problem is transformed into several interval arithmetic and deterministic optimizations, which could enhance computational efficiency without losing much accuracy. The novelty of the proposed method lies in two main aspects. First, an alternate updating strategy is proposed to identify the radii and midpoints of the interval inputs in each cycle, which could reduce the number of iterative steps. Second, the standard quadratic models are constructed based on the dimension-reduction analysis results, rather than the second-order Taylor expansion. Therefore, the interval arithmetic can be applied to efficiently calculate the interval response, which avoids the inner optimization. Moreover, a novel iterative mechanism is developed to accelerate the convergence rate of the proposed method. Finally, two numerical examples and an engineering application are adopted to verify its feasibility, accuracy and efficiency.

关键词： Uncertain inverse problem Interval model sequential quadratic programming Dimension -reduction analysis

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Training mode of university dance performers based on sequential quadratic programming algorithm

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JOURNAL OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2024年第2期24卷 779-795页

作者： Ma, Yujiang Lanzhou Univ Arts & Sci Sch Arts Lanzhou Gansu Peoples R China

Dance performance is an art form, which needs to cultivate students' dance skills, artistic accomplishment and stage performance ability. sequential quadratic programming algorithm is an optimization algorithm that can be used to solve complex optimization problems. In this paper, sequential quadratic programming (SQP) is applied to explore the training mode of dance performers in colleges to help dance performers develop the optimal training plan and program. Aiming at the problems existing in the training mode of dance performance talents in colleges, this paper put forward an optimization method based on SQP algorithm, and implemented its optimization scheme in actual colleges. In the planning of dance performance talent training mode, particle swarm optimization (PSO) is used to optimize SQP algorithm, so that it can have higher planning efficiency. This paper studied the goal and index system of the training of dance performance talents in colleges, generated a personalized training program, and further improved the scientific and practical effectiveness of the training mode. This paper investigated the current situation of dance performance talent training in several dance schools in a certain province of China. The survey data include practical curriculum planning, teachers' teaching philosophy and teaching content. Combined with SQP algorithm, the teaching and training program is optimized. After evaluation, it can be concluded that the SQP algorithm optimized by PSO shows good stability and accuracy. It can calculate the optimal solution of the cultivation scheme, and when calculating the optimal solution, the running time of the Central Processing Unit (CPU) was only 5.6 s, which can further improve the efficiency of the planning. Finally, through the satisfaction and resource utilization test, it can be found that the number of people who are very satisfied with the teaching content of the dance performance talent training program optimized by SQP increas

关键词： Talent training model dance performance in colleges sequential quadratic programming resource allocation effect evaluation particle swarm optimization

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A STRATEGY FOR GLOBAL CONVERGENCE IN A sequential quadratic-programming ALGORITHM

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SIAM JOURNAL ON NUMERICAL ANALYSIS 1989年第3期26卷 600-623页

作者： BOGGS, PT TOLLE, JW UNIV N CAROLINA DEPT MATHCHAPEL HILLNC 27599 UNIV N CAROLINA DEPT OPERAT RESCHAPEL HILLNC 27599

n a previous work [P. Boggs and J. Tolle, SIAM J. Numer. Anal., 21 (1984), pp. 1146–1161], the authors introduced a merit function for use with the sequential quadratic programming (SQP) algorithm for solving nonlinear programming problems. Here, further theoretical justification, including a global convergence theorem, is provided. In addition, modifications are suggested that allow the efficient implementation of the merit function while maintaining the important convergence properties. Numerical results are presented demonstrating the effectiveness of the procedure.

关键词： 90C30 65K05 nonlinear programming problems sequential quadratic programming merit functions

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A sequential quadratic-programming ALGORITHM UTILIZING QR MATRIX FACTORIZATION

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ENGINEERING OPTIMIZATION 1994年第4期22卷 283-296页

作者： KAO, CA CHEN, SP [a]Graduate School of Industrial Management National Cheng Kung University Tainan Taiwan Republic of China

Some recent studies indicate that the sequential quadratic programming (SQP) approach has a sound theoretical basis and promising empirical results for solving general constrained optimization problems. This paper presents a variant of the SQP method which utilizes QR matrix factorization to solve the quadratic programming subproblem which result from taking a quadratic approximation of the original problem. Theoretically, the QR factorization method is more robust and computationally efficient in solving quadratic programs. To demonstrate the validity of this variant, a computer program named SQR is coded in Fortran to solve twenty-eight test problems. By comparing with three other algorithms: one multiplier method, one GRG-type method, and another SQP-type method, the numerical results show that. in general, SQR as devised in this paper is the best method as far as robustness and speed of convergence are concerned in solving general constrained optimization problems.

关键词： CONSTRAINED OPTIMIZATION sequential quadratic programming QR FACTORIZATION

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A sequential quadratic programming based strategy for particle swarm optimization on single-objective numerical optimization

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COMPLEX & INTELLIGENT SYSTEMS 2024年第2期10卷 2421-2443页

作者： Hong, Libin Yu, Xinmeng Tao, Guofang Ozcan, Ender Woodward, John Hangzhou Normal Univ Sch Informat Sci & Technol 2318 Yuhangtang Rd Hangzhou 31121 Peoples R China Univ Nottingham Sch Comp Sci Wollaton Rd Nottingham NG8 1BB England Univ Loughborough Dept Comp Sci Epinal Way Loughborough LE11 3TU England

Over the last decade, particle swarm optimization has become increasingly sophisticated because well-balanced exploration and exploitation mechanisms have been proposed. The sequential quadratic programming method, which is widely used for real-parameter optimization problems, demonstrates its outstanding local search capability. In this study, two mechanisms are proposed and integrated into particle swarm optimization for single-objective numerical optimization. A novel ratio adaptation scheme is utilized for calculating the proportion of subpopulations and intermittently invoking the sequential quadratic programming for local search start from the best particle to seek a better solution. The novel particle swarm optimization variant was validated on CEC2013, CEC2014, and CEC2017 benchmark functions. The experimental results demonstrate impressive performance compared with the state-of-the-art particle swarm optimization-based algorithms. Furthermore, the results also illustrate the effectiveness of the two mechanisms when cooperating to achieve significant improvement.

关键词： Particle swarm optimization Ratio adaptation scheme sequential quadratic programming Single-objective numerical optimization

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Solving the Cutting-Stock Problem by Using the sequential quadratic programming Optimization Method

Solving the Cutting-Stock Problem by Using the Sequential Qu...

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IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)

作者： Lin, T. Y. Chen, S. M. Yu, M. T. Natl Def Univ Dept Mech & Aerosp Engn Taoyuan Taiwan Luren Precis Co Ltd Hsinchu Taiwan

ISBN: (纸本)9781509036653

In operations research, the cutting-stock problem is an important issue in the manufacturing of textile, leather, paper, ship building, and sheet metal industries. This problem arranges the specific profiles on the material with minimum material wasted. It can increase the utility rate and reduce the cost of the stock. For example in the leather industry, the stock has irregular profiles, and the base material may also be irregular when using the remainders of the last cut. In this paper, the problem is formulated as a constrained optimization problem and solved by the sequential quadratic programming (SQP) method. A global optimization algorithm is also proposed to avoid the local minimum point, which is helpful for the multi-stock problem.

关键词： cutting-stock problem global optimization operations research sequential quadratic programming

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An active set sequential quadratic programming algorithm for nonlinear optimisation

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BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY 2006年第1期74卷 69-83页

作者： Hu, Qing-Jie Xiao, Yun-Hai Chen, Y. Hunan Univ Inst Appl Math Changsha 410082 Peoples R China Hunan Business Coll Dept Informat Changsha 410205 Peoples R China

In this paper, we have proposed an active set feasible sequential quadratic programming algorithm for nonlinear inequality constraints optimization problems. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving a reduced quadratic programming subproblem. To overcome the Maratos effect, a higher-order correction direction is obtained by solving a reduced least square problem. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without strict complementarity.

关键词： sequential quadratic programming Least squares method higher-order algorithms quadratic programming Complementarity descent iterative methods inequality constraint

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Constrained particle swarm optimisation for sequential quadratic programming

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2009年第4期8卷 361-367页

作者： Richards, Zach D. United Launch Alliance Littleton CO 80127 USA

sequential quadratic programming (SQP) methods are commonly used to solve constrained non-linear optimisation problems. However, in recent years there has been great improvement in using evolutionary algorithms to solve non-linear optimisations problems. The difficulty has been determining a correct method for implementing evolutionary algorithm for a non-linear optimisation problem with constraints. In this paper, we are combining the strengths of the traditional SQP method with an evolutionary algorithm, particle swarm optimisation (PSO) for solving a constrained non-linear optimisation problem with equality and inequality constraints. We propose a constrained PSO algorithm be used to solve the quadratic programming (QP) subproblem within the SQP method.

关键词： non-linear optimisation particle swarm sequential quadratic programming SQP infeasibility function quadratic subproblem hybrid optimisation non-linear constrained particle swarm optimisation algorithm NLCPSOA

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