CAJ | 학술논문

根据开放式方程模型结构统一、所得优化命题普遍稀疏的特点,提出了一种稀疏SQP算法.利用一阶/二阶导数构造Hessian矩阵,保持了系统的稀疏结构.通过一个预处理过程获得命题的稀疏结构信息,显著减少构造高维矩阵所需工作量.计算示例表明,该算法优于传统SQP法,也表明该算法的有效性.
근거개방식방정모형결구통일、소득우화명제보편희소적특점,제출료일충희소SQP산법.이용일계/이계도수구조Hessian구진,보지료계통적희소결구.통과일개예처리과정획득명제적희소결구신식,현저감소구조고유구진소수공작량.계산시례표명,해산법우우전통SQP법,야표명해산법적유효성.
Chemical process optimization problems based on the open-equation modeling approach are frequently characterized by large sparse models. To solve large-scale on-line optimization problems, efficient and reliable optimization algorithms should be developed and considered. In this paper, a full space sparse SQP algorithm is presented. First/second finite derivatives are used to build Jacobian and Hessian matrices,while the inherent sparse structure existing in systems is maintained. A preprocess is employed to exploit the sparse structure. Through this phase, the elements in Jacobian and Hessian matrices are divided into two parts: zero and nonzero ones. Only nonzero elements are computed in the algorithm. Moreover, to reduce the computing time for Jacobian and Hessian matrices, the constants are identified and withdrew from nonzero elements. Those constant elements are stored as global variables so that they can be called at any time without being computed in each iteration. Thus the computational demands and storage requirements for large matrices could be reduced. Compared with traditional SQP algorithm, the performance of this algorithm is enhanced significantly. These enhancements are demonstrated on a number of test problems, including scalable mathematical problems and chemical optimization problems. Computing results indicate the possibility and efficiency of this algorithm for the large-scale on-line optimization of chemical process systems.