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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 Fast Algorithm for Maximum Likelihood Estimation of Mixture Proportions Using sequential quadratic programming

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2020年第2期29卷 261-273页

作者： Kim, Youngseok Carbonetto, Peter Stephens, Matthew Anitescu, Mihai Univ Chicago Dept Stat Chicago IL 60637 USA Univ Chicago Dept Human Genet Chicago IL 60637 USA Univ Chicago Res Comp Ctr Chicago IL 60637 USA Argonne Natl Lab Math & Comp Sci Div 9700 S Cass Ave Lemont IL 60439 USA

Maximum likelihood estimation of mixture proportions has a long history, and continues to play an important role in modern statistics, including in development of nonparametric empirical Bayes methods. Maximum likelihood of mixture proportions has traditionally been solved using the expectation maximization (EM) algorithm, but recent work by Koenker and Mizera shows that modern convex optimization techniques-in particular, interior point methods-are substantially faster and more accurate than EM. Here, we develop a new solution based on sequential quadratic programming (SQP). It is substantially faster than the interior point method, and just as accurate. Our approach combines several ideas: first, it solves a reformulation of the original problem;second, it uses an SQP approach to make the best use of the expensive gradient and Hessian computations;third, the SQP iterations are implemented using an active set method to exploit the sparse nature of the quadratic subproblems;fourth, it uses accurate low-rank approximations for more efficient gradient and Hessian computations. We illustrate the benefits of the SQP approach in experiments on synthetic datasets and a large genetic association dataset. In large datasets (n approximate to 106observations,m approximate to 103mixture components), our implementation achieves at least 100-fold reduction in runtime compared with a state-of-the-art interior point solver. Our methods are implemented in Julia and in an R package available on CRAN (). Supplementary materials for this article are available online.

关键词： Active set methods Convex optimization Mixture models Nonparametric empirical Bayes Rank-revealing QR decomposition sequential quadratic programming

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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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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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Optimization of Turning Operations by Using a Hybrid Genetic Algorithm with sequential quadratic programming

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JOURNAL OF APPLIED RESEARCH AND TECHNOLOGY 2013年第1期11卷 88-94页

作者： Belloufi, A. Assas, M. Rezgui, I. Univ Mohamed Khider Dept Mech Engn Biskra 07000 Algeria Univ Hadj Lakhder Dept Mech Engn Lab Rech Prod Batna Algeria Univ Kasdi Merbah Ouargla Ouargla Algeria

The determination of optimal cutting parameters is one of the most important elements in any process planning of metal parts. In this paper, a new hybrid genetic algorithm by using sequential quadratic programming is used for the optimization of cutting conditions. It is used for the resolution of a multipass turning optimization case by minimizing the production cost under a set of machining constraints. The genetic algorithm (GA) is the main optimizer of this algorithm whereas SQP Is used to fine tune the results obtained from the GA. Furthermore, the convergence characteristics and robustness of the proposed method have been explored through comparisons with results reported in literature. The obtained results indicate that the proposed hybrid genetic algorithm by using a sequential quadratic programming is effective compared to other techniques carried out by different researchers.

关键词： multipass turning genetic algorithm sequential quadratic programming optimization of cutting conditions

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A ROBUST sequential quadratic-programming METHOD

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MATHEMATICAL programming 1989年第3期43卷 277-303页

作者： BURKE, JV HAN, SP UNIV ILLINOIS DEPT MATHURBANAIL 61801

The sequential quadratic programming method developed by Wilson, Han and Powell may fail if the quadratic programming subproblems become infeasible, or if the associated sequence of search directions is unbounded. This paper considers techniques which circumvent these difficulties by modifying the structure of the constraint region in the quadratic programming subproblems. Furthermore, questions concerning the occurrence of an unbounded sequence of multipliers and problem feasibility are also addressed.

关键词： nonlinear programming sequential quadratic programming

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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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sequential quadratic programming for development of a new probiotic dairy tofu with glucono-δ-lactone

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JOURNAL OF FOOD SCIENCE 2004年第7期69卷 E344-E350页

作者： Chen, MJ Chen, KN Lin, CW Natl Taiwan Univ Dept Anim Sci Taipei 106 Taiwan Tung Nan Inst Technol Dept Mech Engn Taipei Taiwan

The purpose of this research was to evaluate the effects of various concentrations of glucono-delta-lactone (GDL) and skim milk powder, as well as the addition of prebiotics, on the theology and problotic viabilities of dairy tofu. Additionally, modern optimization techniques were applied to attempt to determine the optimal processing conditions and growth rate for the selected probiotics (Lactobacillus. acidophilus, L. casei, Bifidobacteria bifidum, and B. longum). There were 2 stages in this research to accomplish the goal. The 1st stage was to derive surface models using response surface methodology (RSM);the 2nd stage performed optimization on the models using sequential quadratic programming (SQP) techniques. The results were demonstrated to be effective. The most favorable production conditions of dairy tofu were 1% GDL, 0% peptides, 3% isomaltooligosaccharides (IMO), and 18% milk, as confirmed by subsequent verification experiments. Analysis of the sensory evaluation results revealed no significant difference between the probiotic dairy tofu and the GDL analog in terms of texture and appearance (P > 0.05). The viable numbers of probiotics were well above the recommended limit of 10(6) CFU/g for the probiotic dairy tofu throughout the tested storage period.

关键词： sequential quadratic programming glucono-delta-lactone probiotics dairy tofu

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Moving Horizon Optimization of Train Speed Profile Based on sequential quadratic programming

Moving Horizon Optimization of Train Speed Profile Based on ...

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International Conference on Intelligent Rail Transportation (ICIRT)

作者： Liu, Xiaoyu Xun, Jing Ning, Bin Liu, Tong Xiao, Xiao Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing Peoples R China Traff Control Technol Co Ltd Beijing Res Inst Beijing Peoples R China

ISBN: (纸本)9781538675281

Recommended speed profile is a complementary function of the automatic train operation (ATO). Most studies focus on the off-line optimization of recommended speed profile. In this paper, we design a moving horizon optimization algorithm which can get the speed profile online. We use the velocity and operation time as state variables of the nonlinear train operation model and take the energy consumption and punctuality as objectives. Then we apply the sequential quadratic programming (SQP) to such multi-objective optimization problem with several nonlinear constraints. The simulation results based on the Yizhuang Line of Beijing Subway indicate that, the sequential quadratic programming based moving horizon optimization algorithm has high computational efficiency and can make a trade-off between the energy consumption and punctuality.

关键词： train speed profile optimization moving horizon optimization sequential quadratic programming nonlinear system urban rail transit

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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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