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Seismic Design of Structures by sequential quadratic programming with Trust Region Strategy and Endurance Time Method

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KSCE JOURNAL OF CIVIL ENGINEERING 2024年第11期28卷 5104-5115页

作者： Feng, Yue Hainan Univ Dept Civil Engn & Architecture Hainan 570228 Peoples R China

The optimal design of structures subjected to seismic loading poses significant challenges due to the presence of high nonlinearity and computational complexity. To address these challenges, this paper presents a novel methodology that combines sequential quadratic programming with Trust-Region strategy (SQP-TR) and Endurance Time Method (ETM). SQP-TR is initially presented as a numerical optimization approach to address optimization problems by linearizing the constraints and approximating the objective function with Taylor expansion, as well as employing the filter method and trust region strategy to ensure convergence and feasibility. A five-story linear frame validates its effectiveness and demonstrates promising outcomes. ETM is successfully implemented as a seismic analysis approach to perform nonlinear time history analyses in order to capture the dynamic input feature of the seismic load and evaluate the nonlinear dynamic behaviors of structures. Its practical application is demonstrated by a nine-story structure with nonlinearity, which shows satisfactory results. Finally, the proposed methodology is applied to optimize a twelve-story three-Dimensional (3D) Reinforced Concrete (RC) nonlinear building under seismic load, and the results demonstrate that the method can accomplish optimal seismic design with high accuracy and efficiency.

关键词： Optimization Seismic sequential quadratic programming Trust region Endurance time analysis

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Inequality constrained stochastic nonlinear optimization via active-set sequential quadratic programming

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MATHEMATICAL programming 2023年第1-2期202卷 279-353页

作者： Na, Sen Anitescu, Mihai Kolar, Mladen Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA Int Comp Sci Inst Berkeley CA 94704 USA Argonne Natl Lab Math & Comp Sci Div Argonne WI USA Univ Chicago Booth Sch Business Chicago IL USA

We study nonlinear optimization problems with a stochastic objective and deterministic equality and inequality constraints, which emerge in numerous applications including finance, manufacturing, power systems and, recently, deep neural networks. We propose an active-set stochastic sequential quadratic programming (StoSQP) algorithm that utilizes a differentiable exact augmented Lagrangian as the merit function. The algorithm adaptively selects the penalty parameters of the augmented Lagrangian, and performs a stochastic line search to decide the stepsize. The global convergence is established: for any initialization, the KKT residuals converge to zero almost surely. Our algorithm and analysis further develop the prior work of Na et al. (Math Program, 2022. https://***/10.1007/s10107-022-01846-z). Specifically, we allow nonlinear inequality constraints without requiring the strict complementary condition;refine some of designs in Na et al. (2022) such as the feasibility error condition and the monotonically increasing sample size;strengthen the global convergence guarantee;and improve the sample complexity on the objective Hessian. We demonstrate the performance of the designed algorithm on a subset of nonlinear problems collected in CUTEst test set and on constrained logistic regression problems.

关键词： Inequality constraints Stochastic optimization Exact augmented Lagrangian sequential quadratic programming

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Bio-inspired heuristics hybrid with sequential quadratic programming and interior-point methods for reliable treatment of economic load dispatch problem

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NEURAL COMPUTING & APPLICATIONS 2019年第1期31卷 447-475页

作者： Raja, Muhammad Asif Zahoor Ahmed, Usman Zameer, Aneela Kiani, Adiqa Kausar Chaudhary, Naveed Ishtiaq COMSATS Inst Informat Technol Dept Elect Engn Attock Pakistan Pakistan Inst Engn & Appl Sci Dept Comp & Informat Sci Nilore Pakistan Fed Urdu Univ Arts Sci & Technol Dept Econ Islamabad Pakistan Int Islamic Univ Dept Elect Engn Islamabad Pakistan

In the present study, bio-inspired computational heuristics are exploited for finding the solution of economic load dispatch (ELD) problem with valve point loading effect using variants of genetic algorithm (GA) hybrid with sequential quadratic programming (SQP) and interior-point algorithms (IPAs). Variants of GAs are constructed using different sets of routines for its fundamental operators in order to explore the entire search space for global optimum solutions while SQP and IPA are integrated with GAs for rapid local convergence. Nine variants of each design scheme based on GAs, GA-SQP and GA-IPAs are applied on three different ELD problems of thermal power plant systems. Comparative studies of the proposed schemes are performed through the results of statistical performance indices in order to establish the worth and effectiveness in terms of accuracy, convergence and complexity measures.

关键词： Economic load dispatch Hybrid computing Evolutionary computations Genetic algorithms sequential quadratic programming Interior-point algorithms

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An integrated perturbation analysis and sequential quadratic programming approach for Model Predictive Control

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AUTOMATICA 2009年第10期45卷 2412-2418页

作者： Ghaemi, Reza Sun, Jing Kolmanovsky, Ilya V. Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48109 USA Univ Michigan Dept Naval Architecture & Marine Engn Ann Arbor MI 48109 USA Ford Motor Co Dearborn MI 48124 USA

Computationally efficient algorithms are critical in making Model Predictive Control (MPC) applicable to broader classes of systems with fast dynamics and limited computational resources. In this paper, we propose an integrated formulation of Perturbation Analysis and sequential quadratic programming (InPA-SQP) to address the constrained optimal control problems. The proposed algorithm combines the complementary features of perturbation analysis and SQP in a single unified framework, thereby leading to improved computational efficiency and convergence property. A numerical example is reported to illustrate the proposed method and its computational effectiveness. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Nonlinear MPC Fast MPC Neighboring Extremal Optimal Control sequential quadratic programming

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Application of sequential quadratic programming based on active set method in cleaner production

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CLEAN TECHNOLOGIES AND ENVIRONMENTAL POLICY 2022年第1期24卷 413-422页

作者： Xia, Li Ling, Jianyang Xu, Zhen Bi, Rongshan Zhao, Wenying Xiang, Shuguang Qingdao Univ Sci & Technol Coll Chem Engn State Key Lab Base Ecochem Engn Zhengzhou Rd 53 Qingdao 266042 Peoples R China Qilu Normal Univ Chem & Chem Engn Fac Jinan 250013 Shandong Peoples R China

On the platform of general chemical process simulation software (it was named Optimization Engineer, OPEN), a general optimization algorithm for chemical process simulation is developed using C + + code. The algorithm is based on sequential quadratic programming (SQP). We adopt the activity set algorithm and the rotation axis algorithm to generate the activity set to solve the quadratic programming sub-problem. The active set method can simplify the number of constraints and speed up the calculation. At the same time, we used limited memory BFGS algorithm (L-BFGS) to simplify the solution of second derivative matrix. The special matrix storage mode of L-BFGS algorithm can save the storage space and speed up the computing efficiency. We use exact penalty function and traditional step-size rule in the algorithm. These two methods can ensure the convergence of the algorithm, a more correct search direction and suitable search step. The example shows that the advanced optimization function can meet the requirements of General Chemical Process Calculation. The number of iterations can reduce by about 6.0%. The computation time can reduce by about 6.5%. We combined this algorithm with chemical simulation technology to develop the optimization function of chemical engineering simulation. This optimization function can play an important role in the process optimization calculation aiming at energy saving and green production.

关键词： sequential quadratic programming Active set method Chemical process simulation Chemical optimization Green production

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Stress-constrained topology optimization of continuum structures subjected to harmonic force excitation using sequential quadratic programming

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2019年第5期59卷 1747-1759页

作者： Long, Kai Wang, Xuan Liu, Hongliang North China Elect Power Univ Beijing Key Lab Energy Safety & Clean Utilizat Beijing 102206 Peoples R China North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewabl Beijing 102206 Peoples R China Dalian Univ Technol Dept Engn Mech State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

In this paper, we propose a method for stress-constrained topology optimization of continuum structure sustaining harmonic load excitation using the reciprocal variables. In the optimization formulation, the total volume is minimized with a given stress amplitude constraint. The p-norm aggregation function is adopted to treat the vast number of local constraints imposed on all elements. In contrast to previous studies, the optimization problem is well posed as a quadratic program with second-order sensitivities, which can be solved efficiently by sequential quadratic programming. Several numerical examples demonstrate the validity of the presented method, in which the stress constrained designs are compared with traditional stiffness-based designs to illustrate the merit of considering stress constraints. It is observed that the proposed approach produces solutions that reduce stress concentration at the critical stress areas. The influences of varying excitation frequencies, damping coefficient and force amplitude on the optimized results are investigated, and also demonstrate that the consideration of stress-amplitude constraints in resonant structures is indispensable.

关键词： Topology optimization Harmonic analysis p-norm Solid isotropic material with penalization Stress constraints sequential quadratic programming

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Solution of the 2-dimensional Bratu problem using neural network, swarm intelligence and sequential quadratic programming

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NEURAL COMPUTING & APPLICATIONS 2014年第7-8期25卷 1723-1739页

作者： Raja, Muhammad Asif Zahoor Ahmad, Siraj-ul-Islam Samar, Raza COMSATS Inst Informat Technol Dept Elect Engn Attock Pakistan Pakistan Inst Engn & Appl Sci Islamabad Pakistan COMSATS Inst Informat Technol Dept Phys Islamabad Pakistan Mohammad Ali Jinnah Univ Islamabad Pakistan

In this paper, stochastic techniques have been developed to solve the 2-dimensional Bratu equations with the help of feed-forward artificial neural networks, optimized with particle swarm optimization (PSO) and sequential quadratic programming (SQP) algorithms. A hybrid of the above two algorithms, referred to as the PSO-SQP method is also studied. The original 2-dimensional equations are solved by first transforming them into equivalent one-dimensional boundary value problems (BVPs). These are then modeled using neural networks. The optimization problem for training the weights of the network has been addressed using particle swarm techniques for global search, integrated with an SQP method for rapid local convergence. The methodology is evaluated by applying on three different test cases of BVPs for the Bratu equations. Monte Carlo simulations and extensive analyses are carried out to validate the accuracy, convergence and effectiveness of the schemes. A comparative study of proposed results is made with available exact solution, as well as, reported numerical results.

关键词： 2-Dimensional Bratu equations Neural networks Particle swarm optimization Nonlinear ODEs Memetic computing sequential quadratic programming

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A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 1998年第1期10卷 5-34页

作者： Fukushima, M Luo, ZQ Pang, JS Kyoto Univ Grad Sch Engn Dept Appl Math & Phys Kyoto 60601 Japan McMaster Univ Dept Elect & Comp Engn Commun Res Lab Hamilton ON L8S 4K1 Canada Johns Hopkins Univ Whiting Sch Engn Dept Math Sci Baltimore MD 21218 USA

This paper presents a sequential quadratic programming algorithm for computing a stationary point of a mathematical program with linear complementarity constraints. The algorithm is based on a reformulation of the complementarity condition as a system of semismooth equations by means of Fischer-Burmeister functional, combined with a classical penalty function method for solving constrained optimization problems. Global convergence of the algorithm is established under appropriate assumptions. Some preliminary computational results are reported.

关键词： mathematical programs with equilibrium constraints sequential quadratic programming linear complementarity

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A structured reduced sequential quadratic programming and its application to a shape design problem

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 1998年第1期11卷 81-100页

作者： Herdman, TL Kang, KH Virginia Polytech Inst & State Univ Interdisciplinary Ctr Appl Math Blacksburg VA 24061 USA

The objective of this work is to solve a model one dimensional duct design problem using a particular optimization method. The design problem is formulated as an equality constrained optimization, called all at once method, so that the analysis problem is not solved until the optimal design is reached. Furthermore, the sparsity structure in the Jacobian of the linearized constraints is exploited by decomposing the variables into the design and flow parts. To achieve this, sequential quadratic programming with BFGS update for the reduced Hessian of the Lagrangian function is used with the variable reduction method which preserves the structure of the Jacobian in representing the null space basis matrix. By updating the reduced Hessians of which the dimension is the number of design variables, the storage requirement for the Hessians is reduced by a large amount. In addition, the flow part of the Jacobian can be computed analytically. The algorithm with a line search globalization is described. A global and local analysis is provided with a modification of the paper by Byrd and Nocedal [Mathematical programming 49(1991) pp 285-323] in which they analyzed a similar algorithm with the orthogonal factorization method which assumes the orthogonality of the null space basis matrix. Numerical results are obtained and compared favorably with results from the black box method, unconstrained optimization formulation.

关键词： Shape Optimization sequential quadratic programming nonlinear programming variable reduction method

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Integrated Intelligence of Fractional Neural Networks and sequential quadratic programming for Bagley-Torvik Systems Arising in Fluid Mechanics

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JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS 2020年第5期15卷 051003页

作者： Raja, Muhammad Asif Zahoor Manzar, Muhammad Anwaar Shah, Syed Muslim Chen, YangQuan COMSATS Univ Islamabad Dept Elect & Comp Engn Attock Campus Attock 43600 Pakistan Hamdard Univ Islamabad Hamdard Inst Engn & Technol Islamabad 44000 Pakistan Capital Univ Sci & Technol Dept Elect Engn Islamabad 44000 Pakistan Univ Calif Sch Engn 5200 North Lake Rd Merced CA 95343 USA

In this study, an efficient soft computing paradigm is presented for solving Bagley-Torvik systems of fractional order arising in fluid dynamic model for the motion of a rigid plate immersed in a Newtonian fluid using feed-forward fractional artificial neural networks (FrANNs) and sequential quadratic programming (SQP) algorithm. The strength of FrANNs has been utilized to construct an accurate modeling of the equation using approximation theory in mean square error sense. Training of weights of FrANNs is performed with SQP techniques. The designed scheme has been examined on different variants of the systems. The comparative studies of the proposed solutions with available exact as well as reference numerical results demonstrate the worth and effectiveness of the solver. The accuracy, consistency, and complexity are evaluated in depth through results of statistics.

关键词： Bagley-Torvik equation fractional differential equations neural networks artificial Intelligence sequential quadratic programming

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