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A robust implementation of a sequential quadratic programming algorithm with successive error restoration

OPTIMIZATION LETTERS 2011年第2期5卷 283-296页

作者： Schittkowski, K. Univ Bayreuth Dept Comp Sci D-95440 Bayreuth Germany

We consider sequential quadratic programming methods for solving constrained nonlinear programming problems. It is generally believed that these methods are sensitive to the accuracy by which partial derivatives are provided. One reason is that differences of gradients of the Lagrangian function are used for updating a quasi-Newton matrix, e.g., by the BFGS formula. The purpose of this paper is to show by numerical experimentation that the method can be stabilized substantially. The algorithm applies non-monotone line search and internal and external restarts in case of errors due to inaccurate derivatives while computing the search direction. Even in case of large random errors leading to partial derivatives with at most one correct digit, termination subject to an accuracy of 10(-7) can be achieved in 90% of 306 problems of a standard test suite. On the other hand, the original version with monotone line search and without restarts solves only 30% of these problems under the same test environment. In addition, we show how initial and periodic scaled restarts improve the efficiency in situations with slow convergence.

关键词： SQP sequential quadratic programming Nonlinear programming Line search Restart Numerical algorithm Noisy functions

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Sinogram restoration based on shape property in computed tomography

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Informatics in Medicine Unlocked 2020年 20卷

作者： Ri, Hwisong Kim, Jongchol Lee, Muchol Hwang, Hyok Pak, Jonghyok Department of Electronic Engineering Kim Chaek University of Technology Pyongyang 999093 North Korea Department of Control Science University of Science Pyongyang 999093 North Korea Northeastern University Department of Humanities and Law Shenyang 430074 Liaoning China

Low-dose computed tomography (CT) image sequences, obtained to reduce the risk of radiation exposure, can be seriously degraded by quantum noise and other kinds of mechanical and electrical effects. In order to overcome this problem, we firstly present a sinogram restoration algorithm based on nonlinear optimization programs (NLP), including sequential quadratic programming (SQP) and the interior point method (IPM). Then, the reconstructed image is obtained by a filtered back-projection (FBP) from smoothed projection data. A real-time scan was provided by applying CUDA, which improves calculation speed and precision. The effectiveness and practicability of the proposed method are validated by utilizing a digital phantom and by real clinical data experiments. The advantage of the proposed method over other techniques is demonstrated by means of the peak signal-noise ratio (PSNR) and Euclidean distance from the original image. The experimental results show that the proposed algorithm has excellent performance for low-dose CT imaging analysis. © 2020

关键词： CT Interior point method Nonlinear optimization program sequential quadratic programming Shape property Sinogram

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Discrete-Time Optimal Attitude Control of a Spacecraft with Momentum and Control Constraints

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2018年第1期41卷 199-211页

作者： Phogat, Karmvir Singh Chatterjee, Debasish Banavar, Ravi Indian Inst Technol Syst & Control Engn Room 101ACRE Bldg Bombay 400076 Maharashtra India

An algorithm is proposed to solve optimal control problems arising in attitude control of a spacecraft under state and control constraints. First, the discrete-time attitude dynamics are derived by employing discrete mechanics. Then, the orientation transfer, with initial and final values of the orientation and momentum and the time duration being specified, is posed as an energy-optimal control problem in discrete time, subject to momentum and control constraints. Using variational analysis directly on the Lie group SO(3) (the set of 3 x 3 special orthonormal matrices), first-order necessary conditions for optimality are derived, leading to a constrained two-point boundary value problem. This two-point boundary value problem is solved via a novel multiple shooting technique that employs a root-finding Newton algorithm. Robustness of the multiple shooting technique is demonstrated through a few representative numerical experiments.

关键词： Attitude Dynamics Spacecrafts Pontryagin's Maximum Principle Boundary Value Problems Rotational Kinematics Direct Multiple Shooting Method Attitude Kinematics Quaternions sequential quadratic programming Pseudospectral Methods

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Intelligent computing to solve fifth-order boundary value problem arising in induction motor models

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NEURAL COMPUTING & APPLICATIONS 2018年第7期29卷 449-466页

作者： Ahmad, Iftikhar Ahmad, Fayyaz Raja, Muhammad Asif Zahoor Ilyas, Hira Anwar, Nabeela Azad, Zarqa Univ Gujrat Dept Math Gujrat Pakistan Univ Gujrat Dept Stat Gujrat Pakistan COMSATS Inst Informat Technol Dept Elect Engn Attock Campus Attock Pakistan

In this study, biologically inspired intelligent computing approached based on artificial neural networks (ANN) models optimized with efficient local search methods like sequential quadratic programming (SQP), interior point technique (IPT) and active set technique (AST) is designed to solve the higher order nonlinear boundary value problems arise in studies of induction motor. The mathematical modeling of the problem is formulated in an unsupervised manner with ANNs by using transfer function based on log-sigmoid, and the learning of parameters of ANNs is carried out with SQP, IPT and ASTs. The solutions obtained by proposed methods are compared with the reference state-of-the-art numerical results. Simulation studies show that the proposed methods are useful and effective for solving higher order stiff problem with boundary conditions. The strong motivation of this research work is to find the reliable approximate solution of fifth-order differential equation problems which are validated through strong statistical analysis.

关键词： Induction motor model Active set technique Interior point technique sequential quadratic programming Artificial neural networks

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Design of neuro-computing paradigms for nonlinear nanofluidic systems of MHD Jeffery-Hamel flow

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JOURNAL OF THE TAIWAN INSTITUTE OF CHEMICAL ENGINEERS 2018年 91卷 57-85页

作者： Mehmood, Ammara Nouman-Ul-Haq Zameer, Aneela Ling, Sai Ho Raja, Muhammad Asif Zahoor Pakistan Inst Engn & Appl Sci Dept Elect Engn Islamabad Pakistan Riphah Int Univ Dept Phys Islamabad Pakistan PIEAS Dept Comp & Informat Sci Islamabad 45650 Pakistan Univ Technol Dept Engn & IT Ctr Hlth Technol Sch Biomed Engn Sydney NSW Australia COMSATS Inst Informat Technol Dept Elect Engn Attock 43600 Pakistan

In this paper, a neuro-heuristic technique by incorporating artificial neural network models (NNMs) optimized with sequential quadratic programming (SQP) is proposed to solve the dynamics of nanofluidics system based on magneto-hydrodynamic (MHD) Jeffery-Hamel (JHF) problem involving nano-meterials. Original partial differential equations associated with MHD-JHF are transformed into third order ordinary differential equations based model. Furthermore, the transformed system has been implemented by the differential equation NNMs (DE-NNMs) which are constructed by a defined error function using logsigmoid, radial basis and tan-sigmoid windowing kernels. The parameters of DE-NNM of nanofluidics system are optimized with SQP algorithm. To illustrate the performance of the proposed system, MHD-JHF models with base-fluid water mixed with alumina, silver and copper nanoparticles for different Hartman numbers, Reynolds numbers, angles of the channel and volume fractions with three different proposed DE-NNMs are designed to evaluate. For comparison purpose, the proposed results with reference numerical solutions of Adams solver illustrate their worth. Statistical inferences through different performance indices are given to demostrate the accuracy, stability and robustness of the stochastic solvers. (C) 2018 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

关键词： Magneto-hydrodynamic Jeffery-Hamel flow Artificial neural networks Nanofluids Neurocomputing sequential quadratic programming

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The method for optimisation of gas compressors performance in gas storage systems

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INTERNATIONAL JOURNAL OF OIL GAS AND COAL TECHNOLOGY 2018年第1期17卷 12-33页

作者： Warchol, Michal Swirski, Konrad Ruszczycki, Blazej Wojdan, Konrad Transit Technol SA Warsaw Poland Warsaw Univ Technol Inst Heat Engn Warsaw Poland Polish Acad Sci Nencki Inst Expt Biol Warsaw Poland

We present a computational method for achieving an optimal operation of compressor units used in industrial gas storage systems. The proposed method is capable to operate with a mix of compressor types (i.e., with different operational parameters, different power drives, and different types of construction, e.g., reciprocal and turbocompressors). The goal of the optimisation is to find an optimal compressors configuration and distribution of the compressor loads for each instance of time. The proposed method is based on conversion of a multidimensional discrete-continuous optimisation problem into a set of independent combinatorial and nonlinear optimisation problems. We derive the mathematical foundations of the algorithms. The exemplary results of the application are presented.

关键词： optimisation compressor station dynamic programming sequential quadratic programming SQP gas storage

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Tentacle-Based Guidance for Entry Flight with No-Fly Zone Constraint

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2018年第4期41卷 996-1005页

作者： Liang, Zixuan Ren, Zhang Beihang Univ Sch Astronaut Beijing 100191 Peoples R China Beihang Univ Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China

A tentacle-based guidance method has been proposed for entry flights with the no-fly zone constraint. The proposed method is applicable to zones in general shapes. Simulations have been conducted for four entry missions with various no-fly zones. Results show that the tentacle is capable of suggesting a feasible path for the vehicle. The lateral guidance logic, which combines the tentacle feedback and the heading error, is able to fly the vehicle to the target without entering the no-fly zones. The longitudinal tracking law performs well in following the reference trajectory. Therefore, the proposed guidance method can satisfy both the conventional constraints and the additional no-fly zone constraint. Moreover, the guidance method is demonstrated to be effective when the detection of the threat is delayed, which means that it does not rely on the prior knowledge of no-fly zones. To guarantee the computational performance for guidance commands, the guidance method generates only two tentacles in each lateral guidance cycle.

关键词： Aerodynamic Coefficients Lift Coefficient Active Disturbance Rejection Control Flight Path Angle Lift to Drag Ratio Mobile Robots Earth Algebraic Riccati Equation Heading Angle sequential quadratic programming

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A REGULARIZED FACTORIZATION-FREE METHOD FOR EQUALITY-CONSTRAINED OPTIMIZATION

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SIAM JOURNAL ON OPTIMIZATION 2018年第2期28卷 1613-1639页

作者： Arreckx, Sylvain Orban, Dominique Ecole Polytech GERAD Montreal PQ H3C 3A7 Canada Ecole Polytech Dept Math & Ind Engn Montreal PQ H3C 3A7 Canada

We propose a method for equality-constrained optimization based on a problem in which all constraints are systematically regularized. The regularization is equivalent to applying an augmented Lagrangian method but the linear system used to compute a search direction is reminiscent of regularized sequential quadratic programming. A limited-memory BFGS approximation to second derivatives allows us to employ iterative methods for linear least squares to compute steps, resulting in a factorization-free implementation. We establish global and fast local convergence under weak assumptions. In particular, we do not require the LICQ and our method is suitable for degenerate problems. Preliminary numerical experiments show that a factorization-based implementation of our method exhibits significant robustness while a factorization-free implementation, though not as robust, is promising. We briefly discuss generalizing our framework to other classes of methods and to problems with inequality constraints.

关键词： sequential quadratic programming regularization augmented Lagrangian limited-memory BFGS factorization-free method

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

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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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Some mathematical aspects of price optimisation

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SCANDINAVIAN ACTUARIAL JOURNAL 2018年第5期000卷 379-403页

作者： Hashorva, Enkelejd Ratovomirija, Gildas Tamraz, Maissa Bai, Yizhou Univ Lausanne Dept Actuarial Sci Lausanne Switzerland Vaudoise Assurances Lausanne Switzerland Nankai Univ Sch Math Sci Tianjin Peoples R China

Calculation of an optimal tariff is a principal challenge for pricing actuaries. In this contribution we are concerned with the renewal insurance business discussing various mathematical aspects of calculation of an optimal renewal tariff. Our motivation comes from two important actuarial tasks, namely (a) construction of an optimal renewal tariff subject to business and technical constraints, and (b) determination of an optimal allocation of certain premium loadings. We consider both continuous and discrete optimisation and then present several algorithmic suboptimal solutions. Additionally, we explore some simulation techniques. Several illustrative examples show both the complexity and the importance of the optimisation approach.

关键词： Market tariff optimal tariff price optimisation renewal business sequential quadratic programming

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