Sự hội tụ của thuật toán Ý tưởng trung tâm đằng sau phương pháp tính toán tối ưu hóa là để tìm kiếm cho điểm tối ưu một cách lặp đi lặp lại, tạo ra một chuỗi các thiết kế. Điều quan trọng là cần lưu ý rằng sự thành công của phương pháp phụ thuộc vào việc bảo lãnh của hội tụ của chuỗi điểm tối ưu. | Convergence of Algorithms The central idea behind numerical methods of optimization is to search for the optimum point in an iterative manner generating a sequence of designs. It is important to note that the success of a method depends on the guarantee of convergence of the sequence to the optimum point. The property of convergence to a local optimum point irrespective of the starting point is called global convergence of the numerical method. It is desirable to employ such convergent numerical methods in practice since they are more reliable. For unconstrained problems a convergent algorithm must reduce the cost function at each iteration until a minimum point is reached. It is important to note that the algorithms converge to a local minimum point only as opposed to a global minimum since they only use the local information about the cost function and its derivatives in the search process. Methods to search for global minima are described in Chapter 18. Rate of Convergence In practice a numerical method may take a large number of iterations to reach the optimum point. Therefore it is important to employ methods having a faster rate of convergence. Rate of convergence of an algorithm is usually measured by the numbers of iterations and function evaluations needed to obtain an acceptable solution. Rate of convergence is a measure of how fast the difference between the solution point and its estimates goes to zero. Faster algorithms usually use second-order information about the problem functions when calculating the search direction. They are known as Newton methods. Many algorithms also approximate second-order information using only the first-order information. They are known as quasi-Newton methods described in Chapter 9. Basic Ideas and Algorithms for Step Size Determination Unconstrained numerical optimization methods are based on the iterative formula given in Eq. . As discussed earlier the problem of obtaining the design change Ax is .
