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The Sequential Quadratic Programming (SQP) Algorithm Given a solution estimate xk, and a small step d, an arbitrary numerical optimization problem can be approximated as follow: f(xk+d)=f(xk)+[▽f(xk)] T*d + 1/2*(dT)[▽2f(xk)]*d+.... h(xk+d)=h(xk)+[▽h(xk)]T*d + 1/2*(dT)[▽2h(xk)]*d+.... = 0 g(xk+d)=g(xk)+[▽g(xk)]T*d + 1/2*(dT)[▽2g(xk)]*d+.... >= 0 where x=[x1,x2,…xk]T, d=[d1,d2,…dk]T Form the linearly-constrained/quadratic minimization problem: Minimize: f(xk)+[▽f(xk)]T*d + 1/2*(dT)[▽2f(xk)]*d Subject to: h(xk)+[▽h(xk)]T*d = 0; g(xk)+[▽g(xk)]T*d >=0; In the SQP loop, the approximate QP should be a convex Quadratic Programming, in which the matrix Q = ▽2f(xk) should be positive semidefinite, Q ≥ 0. Actually, the Q is the Hessian matrix of the function f(x) at the point xk.

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"This important volume is the first part of a two-part textbook (the second part is entitled Conservation laws and elliptic equations). The text includes interesting homework problems that implement different aspects of most of the schemes discussed. The implementation aspect of this text includes a large amount of computing. Other useful aspects of computing included in this volume are symbolic computing and the use of graphics for analysis. Prerequisites suggested for using this book might include one semester of partial differential equations and some programming capability. This book will be a good reference text for students." -- MATHEMATICAL REVIEWS

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Numerical Python: Scientific Computing and Data Science Applications with Numpy, SciPy and Matplotlib By 作者: Robert Johansson ISBN-10 书号: 1484242459 ISBN-13 书号: 9781484242452 Edition 版本: 2nd ed. 出版日期: 2018-12-25 pages 页数: (700 ) Work with vectors and matrices using NumPy Plot and visualize data with Matplotlib Perform data analysis tasks with Pandas and SciPy Review statistical modeling and machine learning with statsmodels and scikit-learn Optimize Python code using Numba and Cython Cover Front Matter 1. Introduction to Computing with Python 2. Vectors, Matrices, and Multidimensional Arrays 3. Symbolic Computing 4. Plotting and Visualization 5. Equation Solving 6. Optimization 7. Interpolation 8. Integration 9. Ordinary Differential Equations 10. Sparse Matrices and Graphs 11. Partial Differential Equations 12. Data Processing and Analysis 13. Statistics 14. Statistical Modeling 15. Machine Learning 16. Bayesian Statistics 17. Sinal Processing 18. Data Input and Output 19. Code Optimization

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