非线性非凸L_1－极小化的最优性充分条件

SUFFICIENT OPTIMALITY CONDITIONS FOR NONLINEAR NONCONVEX L_1-MINIMIZATION

讨论一类特殊的非线性非凸Ｌ１－极小化问题：其中一阶连续可微，ｉ＝１，…，ｍ当恒为常数，恒为线性时，（ｐ）退化为校时离散线性Ｌ１－逼近问题．当（Ｘ）但为零时，（Ｐ）为凸复合Ｌ１极小化问题．这两类问题在８０年代已有广泛讨论．在通常情况下，要给出非光滑Ｌ１－极小化的充分条件是困难的，本文利用（Ｐ）的特殊结构给出其极小化的一个最优性充分条件，此可作为排除“伪极小”的一个依据．

kind of nonlinear nonconvcx F_1-minimization problem was considered.The model was a generalization of censored discrete linear L1-approximation discussed by R. S. Womersley and convex L1-minimization model by R. Fletcher and Y.Yuan. The sufficient optimality conditions were presented. The result may be emplogyed in the design of descent Bundle-like algorithms for our problem.