大步长路径跟踪内点新算法

New Interior Point Algorithm with Large-Step Path Following

给出一种求解约束非线性规划问题的大步长路径跟踪内点新算法.首先,为克服内点法初始点选取的困难,通过引入辅助变量来构造原问题的等价问题;其次,构造一个新的关系不等式来证明算法的全局收敛性;最后,在此基础上设计一个新的大步长路径跟踪内点算法.该算法在有限步内能得到原问题的近似最优解,并且数值试验表明,该算法是可行的.

An interior point algorithm based on large-step path following for solving constrained nonlinear programming problem is presented.To overcome the difficulty of initialization in the interior point method,an equivalent problem that incorporates an auxiliary variable is introduced.An inequality is constructed to proof the global convergence.Based on the work done before,a large-step path-following interior point algorithm is established.The proposed algorithm only requires a finite number of iterations to reach a near-optimal solution.Numerical tests are given to show feasibility of the algorithm.