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Introduction to Optimum Design phần 6

Các tài sản của hội tụ đến một điểm tối ưu địa phương không phân biệt của điểm bắt đầu được gọi là hội tụ của phương pháp số toàn cầu. Đó là mong muốn để sử dụng phương pháp hội tụ số trong thực tế vì chúng là đáng tin cậy hơn. | 1. The method should not be used as a black box approach for engineering design problems. The selection of move limits is a trial and error process and can be best achieved in an interactive mode. The move limits can be too restrictive resulting in no solution for the LP subproblem. Move limits that are too large can cause oscillations in the design point during iterations. Thus performance of the method depends heavily on selection of move limits. 2. The method may not converge to the precise minimum since no descent function is defined and line search is not performed along the search direction to compute a step size. Thus progress toward the solution point cannot be monitored. 3. The method can cycle between two points if the optimum solution is not a vertex of the feasible set. 4. The method is quite simple conceptually as well as numerically. Although it may not be possible to reach the precise optimum with the method it can be used to obtain improved designs in practice. 10.4 Quadratic Programming Subproblem As observed in the previous section the SLP is a simple algorithm to solve general constrained optimization problems. However the method has some limitations the major one being the lack of robustness. To correct the drawbacks a method is presented in the next section where a quadratic programming QP subproblem is solved to determine a search direction. Then a step size is calculated by minimizing a descent function along the search direction. In this section we shall define a QP subproblem and discuss a method for solving it. 10.4.1 Definition of QP Subproblem To overcome some of the limitations of the SLP method other methods have been developed to solve for design changes. Most of the methods still utilize linear approximations of Eqs. 10.19 to 10.21 for the nonlinear optimization problem. However the linear move limits of Eq. 10.24 are abandoned in favor of a step size calculation procedure. The move limits of Eq. 10.24 play two roles in the solution