Smooth convex approximation and its applications

In this thesis, we consider a smooth convex approximation to the sum of the $\kappa$ largest components. To make it applicable to a wide class of applications, the study is conducted on some minmax problems. Based on a special smoothing technique, we give an efficient scheme for nonsmooth convex function. By using the composite property of g_\kappa(\varepsilon; \cdot) and eigenvalue function $\Lambda(X)$, we find the smooth approximate function to the sum of the $\kappa$ largest eigenvalue function.

Author dc:creator

• SHI SHENGYUAN

• convex optimization, non-smooth optimization, semismooth function, sum of eigenvalues