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中文摘要：
研究一个新的求解二阶锥规划的一步光滑牛顿法.该算法基于向量最小值函数的新光滑函数,将二阶锥规划问题转化成一个非线性方程组问题,再利用牛顿法求解此方程组.算法不要求初始点及其迭代点严格可行,并且在每一步迭代只需求解一个线性方程组并进行一次线性搜索.在不需要满足严格互补条件下,证明了算法是全局收敛且是局部二阶收敛的.数值试验表明算法是有效的.
英文摘要：
In this paper,a new one-step smoothing Newton method is investigated for solving the second-order cone programming（SOCP）.Based on a new smoothing function of the vector minimum function,the proposed algorithm reformulates the SOCP as a nonlinear system of equations and then applies Newton’s method to the system.This algorithm does not require the initial point and iteration points to be in the sets of strictly feasible solutions,and solves only one linear system of equations and performs only one line search at each iteration.Without strict complementarity,it is proved that the proposed algorithm is globally and locally quadratically convergent.Numerical experiments demonstrate the feasibility and efficiency of our algorithm.
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