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Globally Convergent Optimization Algorithm Using Conservative Convex Separable Diagonal quadratic Approximations

AIAA JOURNAL 2009年第11期47卷 2649-2657页

作者： Groenwold, Albert A. Wood, Derren W. Etman, L. F. P. Tosserams, Simon Univ Stellenbosch Dept Mech & Mechatron Engn ZA-7602 Stellenbosch South Africa Eindhoven Univ Technol Dept Mech Engn NL-5600 MB Eindhoven Netherlands

We implement and test a globally convergent sequential approximate optimization algorithm based on (convexified) diagonal quadratic approximations. The algorithm resides in the class of globally convergent optimization methods based on conservative convex separable approximations developed by Svanberg. At the start of each outer iteration, the initial curvatures of the diagonal quadratic approximations are estimated using historic objective and/or constraint function value information, or by building the diagonal quadratic approximation to the reciprocal approximation at the current iterate. During inner iterations, these curvatures are increased if no feasible descent step can be made. Although this conditional enforcement of conservatism on the subproblems is a relaxation of the strict conservatism enforced by Svanberg, global convergence is still inherited from the conservative convex separable approximations framework developed by Svanberg. A numerical comparison with the globally convergent version of the method of moving asymptotes and the nonconservative variants of both our algorithm and method of moving asymptotes is made.

关键词： sequential quadratic programming Nonlinear programming Messerschmitt Bolkow Blohm Finite Element Method Sensitivity Analysis Structural Optimization Trusses Structural Mechanics Structural Weight FORTRAN

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A multi-stage optimization technique for simultaneous reconstruction of infrared optical and thermophysical parameters in semitransparent media

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INFRARED PHYSICS & TECHNOLOGY 2018年 92卷 219-233页

作者： Sun, Shuang-Cheng Qi, Hong Wang, Shen-Ling Ren, Ya-Tao Ruan, Li-Ming Harbin Inst Technol Sch Energy Sci & Engn 92 West Dazhi St Harbin 150001 Heilongjiang Peoples R China

A multi-stage optimization technique is proposed to simultaneously reconstruct the infrared optical and thermophysical parameters in semitransparent media. The coupled radiative-conductive heat transfer in two-dimensional absorbing, scattering and emitting medium is solved by the discrete ordinate method combined with finite volume method. The exit radiative intensity and temperature distribution on the boundary are served as input for the inverse analysis, and the sequential quadratic programming is used as the inverse technique. Since the measurement signals are much more sensitive to the infrared absorption and scattering coefficients than to the thermal conductivity of medium, the thermophysical property cannot be accurately reconstructed by the conventional method. The multi-stage optimization technique is developed to solve the inverse estimation tasks, through which the optical and thermophysical parameters are reconstructed in different stages based on different objective functions. All the retrieval results demonstrate that the multi-stage optimization technique is robust and effective in simultaneous estimation of absorption coefficient, scattering coefficient and thermal conductivity. The optical and thermophysical parameters can be reconstructed accurately even with measurement errors.

关键词： Multi-stage optimization technique Image reconstruction Infrared optical parameter Thermal conductivity sequential quadratic programming Inverse technique

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A novel PID controller tuning method based on optimization technique

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Journal of Central South University 2010年第5期17卷 1036-1042页

作者：梁昔明李山春 HASSAN A B School of Information Science and Engineering Central South University

An approach for parameter estimation of proportional-integral-derivative(PID) control system using a new nonlinear programming(NLP) algorithm was ***/IIPM algorithm is a sequential quadratic programming(SQP) based algorithm that derives its search directions by solving quadratic programming(QP) subproblems via an infeasible interior point method(IIPM) and evaluates step length adaptively via a simple line search and/or a quadratic search algorithm depending on the termination of the IIPM *** task of tuning PI/PID parameters for the first-and second-order systems was modeled as constrained NLP problem. SQP/IIPM algorithm was applied to determining the optimum parameters for the PI/PID control *** assess the performance of the proposed method,a Matlab simulation of PID controller tuning was conducted to compare the proposed SQP/IIPM algorithm with the gain and phase margin(GPM) method and Ziegler-Nichols(ZN) *** results reveal that,for both step and impulse response tests,the PI/PID controller using SQP/IIPM optimization algorithm consistently reduce rise time,settling-time and remarkably lower overshoot compared to GPM and ZN methods,and the proposed method improves the robustness and effectiveness of numerical optimization of PID control systems.

关键词： PID controller optimization infeasible interior point method sequential quadratic programming simulation

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Complex weight control of array pattern nulling

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INTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING 2007年第3期17卷 304-310页

作者： Mouhamadou, Moctar Vaudon, Patrick Fac Sci & Tech OSA EM Wave & Antennas Dept CNRS UMR 6172XLIM123 Ave Albert Thomas F-87060 Limoges France

An efficient method based on the sequential quadratic programming (SQP) algorithm for the linear antenna arrays pattern synthesis with prescribed nulls in the interference direction and minimum side lobe levels by the complex weights of each array element is presented. In general, the pattern synthesis technique that generates a desired pattern is a greatly nonlinear optimization problem. SQP method is a versatile method to solve the general nonlinear constrained optimization problems and is much simpler to implement. It transforms the nonlinear minimization problem to a sequence of quadratic subproblem that is easier to solve, based on a quadratic approximation of the Lagrangian function. Several numerical results of Chebyshev pattern with the imposed single, multiple, and broad nulls sectors are provided and compared with published results to illustrate the performance of the proposed method. (C) 2007 Wiley Periodicals, Inc.

关键词： null steering antenna array interference suppression sequential quadratic programming pattern synthesis

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Comparison of three unsupervised neural network models for first Painlev, Transcendent

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NEURAL COMPUTING & APPLICATIONS 2015年第5期26卷 1055-1071页

作者： Raja, Muhammad Asif Zahoor Khan, Junaid Ali Shah, Syed Muslim Samar, Raza Behloul, Djilali COMSATS Inst Informat Technol Dept Elect Engn Attock Pakistan Hamdard Univ Fac Engn Sci & Technol Karachi Pakistan Mohammad Ali Jinnah Univ Dept Elect Engn Islamabad Pakistan USTHB Dept Comp Sci Algiers 16111 Algeria

In this paper, a reliable soft computing framework is presented for the approximate solution of initial value problem (IVP) of first Painlev, equation using three unsupervised neural network models optimized with sequential quadratic programming (SQP). These mathematical models are constructed in the form of feed-forward architecture including log-sigmoid, radial base and tan-sigmoid activation functions in the hidden layers. The optimization of designed parameters for each model is performed with SQP, an efficient constraint optimization problem-solving algorithm. The designed methodology is tested on the IVP, and comparative study is carried out with standard solution based on numerical and analytical solvers. The accuracy, convergence and effectiveness of the schemes are validated on the given benchmark problem by large number of simulations and their comprehensive analysis.

关键词： Painleve Transcendents Artificial neural network sequential quadratic programming Nonlinear differential equations Activation functions Unsupervised learning

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Placement and operation strategy of FACTS devices using optimal continuous power flow

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SCIENTIA IRANICA 2012年第6期19卷 1683-1690页

作者： Aghaei, J. Gitizadeh, M. Kaji, M. Shiraz Univ Technol Dept Elect & Elect Engn Shiraz Iran

In this paper, an effective method is presented to determine the security margin against voltage collapse, and improve it by means of FACTS devices in the optimal continuous power flow framework. The primary methods for determining the system's critical states of voltage collapse points are based on the convergence of the Newton-Raphson method in various iterations. Unlike these methods, in this investigation, a method based on sequential quadratic programming is proposed to overcome the divergence of the problem near the critical states, and also to incorporate operation and control constraints through optimal continuous power flow. Furthermore, two FACTS devices, the Thyristor-Controlled Series Capacitor (TCSC) and the Static VAR Compensator (SVC), are mathematically represented and employed in the optimization process to improve the security margin. The proposed method is implemented on a practical power network to investigate the efficacy of the method. (C) 2012 Sharif University of Technology. Production and hosting by Elsevier B.V. All rights reserved.

关键词： Voltage collapse sequential quadratic programming FACTS devices Voltage security margin Optimal continuous power flow

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Computing the nearest low-rank correlation matrix by a simplified SQP algorithm

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APPLIED MATHEMATICS AND COMPUTATION 2015年 256卷 404-414页

作者： Zhu, Xiaojing Shanghai Univ Elect Power Sch Math & Phys Shanghai 200090 Peoples R China

In this paper, we propose a numerical method for computing the nearest low-rank correlation matrix (LRCM). Motivated by the fact that the nearest LRCM problem can be reformulated as a standard nonlinear equality constrained optimization problem with matrix variables via the Gramian representation, we propose a new algorithm based on the sequential quadratic programming (SQP) method. On each iteration, we do not solve the quadratic program (QP) corresponding to the exact Hessian, but a modified QP with a simpler Hessian. This QP subproblem can be solved efficiently by equivalently transforming it to a sparse linear system. Global convergence is established and preliminary numerical results are presented to demonstrate the proposed method is potentially useful. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Low-rank correlation matrix Matrix optimization Nonlinear constrained optimization Gramian representation sequential quadratic programming

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Log Polynomial Velocity Profile for Vertical Landing

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2018年第7期41卷 1617-1623页

作者： Gautam, Alvika Ratnoo, Ashwini Sujit, P. B. Indraprastha Inst Informat Technol Delhi Dept Comp Sci Engn Delhi 110020 India Indian Inst Sci Dept Aerosp Engn Bangalore 560012 Karnataka India Indraprastha Inst Informat Technol Delhi Dept Elect & Commun Engn New Delhi 110020 India Loughborough Univ Aeronaut & Automot Engn Epinal Way Loughborough LE11 3TU Leics England

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An input/output model reduction-based optimization scheme for large-scale systems

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MULTISCALE MODELING & SIMULATION 2005年第2期4卷 691-708页

作者： Luna-Ortiz, E Theodoropoulos, C UMIST Dept Proc Integrat Manchester M60 1QD Lancs England

A reduced model based optimization strategy is presented for the cases where input/ output codes are the process simulators of choice, and thus system Jacobians and even system equations are not explicitly available to the user. The former is the case when commercial software packages or legacy codes are used to simulate a large-scale system and the latter when microscopic or multiscale simulators are employed. When such black-box dynamic simulators are used, we perform optimization by combining the recursive projection method [ G. M. Shroff and H. B. Keller, SIAM J. Numer. Anal., 30 ( 1993), pp. 1099 - 1120] which identifies the ( typically) low-dimensional slow dynamics of the (dissipative) model with a second reduction to the low-dimensional subspace of the decision variables. This results in the solution of a low-order unconstrained optimization problem. Optimal conditions are then computed in an efficient way using only low-dimensional numerical approximations of gradients and Hessians. The tubular reactor is used as an illustrative example to demonstrate this model reduction-based optimization methodology.

关键词： sequential quadratic programming reduced Hessian recursive projection method invariant subspace black-box integrators

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Assessing Accessibility of Main-Belt Asteroids Based on Gaussian Process Regression

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2017年第5期40卷 1144-1154页

作者： Shang, Haibin Liu, Yuxin Beijing Inst Technol Sch Aerosp Engn Key Lab Dynam & Control Flight Vehicle Beijing 100081 Peoples R China Delft Univ Technol Fac Aerosp Engn NL-2629 HS Delft Netherlands

The main-belt asteroids are of great scientific interest and have become one of the primary targets of planetary exploration. In this paper, the accessibility of more than 600,000 main-belt asteroids is investigated. A computationally efficient approach based on Gaussian process regression is proposed to assess the accessibility. Two transfer models consisting of globally optimal two-impulse and Mars gravity-assist transfers are established, which would serve as a source of training samples for Gaussian process regression. The multistart and deflection technologies are incorporated into the numerical optimization solver to avoid local minima, thereby guaranteeing the quality of the training samples. The covariance function, as well as hyperparameters, which dominate the regression process, are chosen elaborately in terms of the correlation between samples. Numerical simulations demonstrate that the proposed method can achieve the accessibility assessment within tens of seconds, and the average relative error is only 1.33%. Mars gravity assist exhibits significant advantage in the accessibility of main-belt asteroids because it reduces the total velocity increment by an average of 1.23 km/s compared with the two-impulse transfer. Furthermore, it is observed that 3976 candidate targets have potential mission opportunities with a total velocity increment of less than 6 km/s.

关键词： Gaussian Process Asteroids Formation and Evolution of the Solar System Numerical Optimization Numerical Simulation sequential quadratic programming Earth Orbital Elements Interplanetary Mission Orbital Inclination

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