【摘要】 主要研究L1/2正则化问题.首先给出了该问题的最优性条件的分析,得到了一阶和二阶必要条件,同时给出了二阶充分条件.这些最优性条件可以看作是光滑函数最优性条件的推广.在此基础上,提出了一种下降算法,并给出了该算法的全局收敛性分析.该算法可以看作是最速下降法的推广.更多还原

【Abstract】 This paper is concerned with the L1/2regularization problem.We first study the optimality conditions for the problem.The optimality conditions obtained are the extensions of the optimality conditions for the minimization of a smooth function.Based on this,we derive a decent direction.We then develop a descent method for solving the problem.The method can be regarded as an extension of the wellknown steepest descent method.Under appropriate conditions,we show that the proposed method is globally convergent.更多还原