一类非线性大系统优化问题的逼近算法

An approximation algorithm for a class of large-scale nonlinear optimization problems

针对一类约束函数是变量可分离的非线性大系统优化问题，本文给出一种基于逐次逼近算法的熵函数法．对每一个子问题，该方法可以通过解一个可微的无约束极小值问题，一次性地获得其ε－ 最优解，避免了序列极小化过程，并且可以通过参数的选取控制解的误差．初步的数值试验表明，对于该类非线性大系统优化问题，本算法有良好的数值表现．

A hybrid algorithm is proposed for a class of large scale nonlinear programming problems with decomposable constraints. The algorithm is based on a successive approximation technique and the so called envelope function method, by which one can obtain an ε optimum for each subproblem by solving just one differentiable unconstrained minimization problem and control the solution error of subproblems by selecting suitable parameters concerned in the envelope function. Preliminary numerical experiments show that the proposed algorithm is effective.