中文摘要：

作为基本数学结构，在对称的锥和它的答案上的不平等的系统能为解决被用来解决许多优化问题的内部点方法的开始问题提供一个有效方法。在这份报纸，一个非内部的继续算法为在一个对称的锥导致的顺序下面解决不平等的系统被建议。建议算法全球性会聚、明确，这被显示出。而且，它能从任何点和仅仅需要开始在每次重复至多解决线性方程的一个系统。在合适的假设下面，全球线性、本地的二次的集中与欧几里德几何学的乔丹代数学被建立。数字结果显示算法是有效的。随机的线性不平等的系统与 10,100 的尺寸在秒顺序锥上被测试， ... ， 1 000 分别地并且每种尺寸的问题在 10 次随机被产生。平均反复的数字证明建议算法能为与随机的初始化解决问题的给定的线性类在一步产生一个解决方案。继续算法能快速在秒顺序锥上解决线性不平等的更大的规模系统，似乎可能。而且，非线性的不平等的一个系统也在二简单秒顺序的笛卡儿的产品上被测试锥，和数字结果显示建议算法能处理非线性的盒子。

英文摘要：

As a basic mathematical structure, the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems. In this paper, a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone. It is shown that the proposed algorithm is globally convergent and well-defined. Moreover, it can start from any point and only needs to solve one system of linear equations at most at each iteration. Under suitable assumptions, global linear and local quadratic convergence is established with Euclidean Jordan algebras. Numerical results indicate that the algorithm is efficient. The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,..., 1 000 respectively and the problems of each size were generated randomly for 10 times. The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations. It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the second- order cones quickly. Moreover, a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones, and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.