非线性规划的人工释能及单变量曲径寻优算法

STUDY ON ARTIFICIAL RELEASE ENERGY METHOD AND ALONG CURVILINEAR SEARCH OF NONLINEAR PROGRAMMING

给出了求解一般不等式约束的非线性规划问题的一个常微分方程的解法（即ＯＤＥ方法）．其一维搜索的路径是约束曲面上的一条最短线，其方程是由变分法建立的一组常微分方程的初值问题所确定的．在初始点（或迭代点）位于可行域内部时，采用人工释能法来求得下一个改进的可行点．数值例子表明该算法具有较好的计算效果．而且，在较弱的条件下给出了该算法的收敛性证明．

Some algorithms are derived from way of solving an system of ordinary differential equations for nonlinear programming problems constrained with general inequality. Its path of one-dimensional search is the geodesics on the boundary surface of the feasible region. The equation of geodesic is presented by an initial-value system of differential equations derived from the calculus of variations. In general,the search path is curvilinear. When the initial iteration point is inside the feasible region,the method of 'artificial release energy' is used. Furthermore,the convergence of our algorithm under weaker conditions is shown. Finally,some numerical examples show that our algorithms have good calculating effect.