CAJ | 학술논문

针对经济与金融中出现的一类特殊非线性比式和问题，给出一种基于单纯形剖分的全局优化算法．在算法中，通过构造初始单纯形，以及使用凸包络理论，提出了一个确定原问题最优值下界的新方法．在确定下界的同时，将会得到原问题的n＋1可行解，这些可行解可以用于上界的改善．理论上证明了算法的收敛性，数值算例表明算法是有效可行的．
침대경제여금융중출현적일류특수비선성비식화문제，급출일충기우단순형부분적전국우화산법．재산법중，통과구조초시단순형，이급사용철포락이론，제출료일개학정원문제최우치하계적신방법．재학정하계적동시，장회득도원문제적n＋1가행해，저사가행해가이용우상계적개선．이론상증명료산법적수렴성，수치산례표명산법시유효가행적．
For solving a special class of nonlinear sum of ratios problem arised in economy and finance, a global optimization algorithm is presented based on simplicial bisection. In this algorithm, by constructing an initial simplex and using convex envelope theory, a new method to determine lower bound of the optimal value for the original problem is proposed. With the determination of the lower bound, n＋ 1 feasible points of the original problem will be found, which can be used to improve upper bound. Convergence of the algorithm is shown and some numerical examples are given to illustrate the feasibility and effectiveness of the presented algorithm.