CAJ | 학술논문

针对线性等式约束优化问题，提出了一种新的移动渐近线算法。先将原问题转为以搜索方向为设计变量的新的优化问题，使用零空间技术处理进一步简化为无约束优化问题。然后，在迭代过程中，构造目标函数的移动渐近线函数且组成优化问题，求解优化问题获得下降搜索方向和搜索步长。我们讨论了算法的参数选取准则，并证明了该算法的全局收敛性。试验结果表明算法是有效地求解大规模的线性约束优化问题。
침대선성등식약속우화문제，제출료일충신적이동점근선산법。선장원문제전위이수색방향위설계변량적신적우화문제，사용령공간기술처리진일보간화위무약속우화문제。연후，재질대과정중，구조목표함수적이동점근선함수차조성우화문제，구해우화문제획득하강수색방향화수색보장。아문토론료산법적삼수선취준칙，병증명료해산법적전국수렴성。시험결과표명산법시유효지구해대규모적선성약속우화문제。
To solve linear equality constrains optimizations, it aims to introduce a new method of moving asymptotes. Firstly, original optimization was converted to a new optimization that was searched direc-tion as design variables. The linear equality constraints functions are coped with null space technique and original constrained optimization is equivalently converted into unconstrained optimization. What’s more, the principle of the proposed algorithm is to construct a new moving asymptotes function in iteration. It obtains the descending direction and the search step by solving this problem. The concrete selection of the parameters is examined. Further, it proves that the algorithm is global convergent. The numerical results show that the algorithm is effective and can be used to deal with some large-scale unconstrained optimiza-tion problems.