Hidden Convex Minimization
Hidden Convex Minimization
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DOI：
10.1007/s10898-004-5697-5
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发表时间：
2005-02
影响因子：
1.8
通讯作者：
Duan Li;Zhiyou Wu;H. J. Joseph Lee;Xinmin Yang;Lian-sheng Zhang
中科院分区：
文献类型：
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作者：
Duan Li;Zhiyou Wu;H. J. Joseph Lee;Xinmin Yang;Lian-sheng Zhang
一类非凸最小化问题可以归类为隐凸最小化问题。如果存在等价变换使得其等价变换是凸最小化问题，则非凸最小化问题称为隐凸最小化问题。本文推导了独立于变换的充分条件，用于识别此类看似非凸的最小化问题，而这些问题等价于凸最小化问题。因此，对于此类隐凸优化问题，可以通过使用局部搜索方法来实现全局最优。本文提出的结果通过识别非凸表示的等价物扩展了凸最小化的范围。
A class of nonconvex minimization problems can be classified as hidden convex minimization problems. A nonconvex minimization problem is called a hidden convex minimization problem if there exists an equivalent transformation such that the equivalent transformation of it is a convex minimization problem. Sufficient conditions that are independent of transformations are derived in this paper for identifying such a class of seemingly nonconvex minimization problems that are equivalent to convex minimization problems. Thus, a global optimality can be achieved for this class of hidden convex optimization problems by using local search methods. The results presented in this paper extend the reach of convex minimization by identifying its equivalent with a nonconvex representation.