一种求解二阶锥规划问题的新算法

为了提高求解二阶锥规划问题的效率,提出一种新的求解二阶锥规划问题的非单调信赖域算法.基于Fischer-Burmeister光滑函数,对二阶锥规划问题的最优性条件进行转化,得到与其等价的无约束优化问题的非线性可微的光滑方程组,构造信赖域子问题,利用非单调信赖域算法求解.算法在求解信赖域子问题时,提出了一个新的自适应选取信赖域半径机制,搜索到全局最优解.数值实验结果表明,该算法运行速度快、迭代次数少,比内点算法和不可行内点算法优越.

A new algorithm for solving second-order cone programming

In order to improve the efficiency of solving the problem of second-order cone programming problem, a new nonmonotonic trust region algorithm is proposed for solving SOCP. Based on the Fischer-Burmeister smoothing function, the optimality conditions of second-order cone programming problem are transformed into unconstrained optimization problem and the trust region subproblem is constructed, a new adaptive mechanism for the trust region radius is presented, the global optimal solution can be got. The numerical results show that the algorithm runs faster and requires fewer iterations, it is superior than the traditional interior-point algorithm and the infeasible interior-point algorithm.