In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and eng...

To efficiently solve online problems with complicated constraints, projection-free algorithms including frank-wolfe (OFW) and its variants have received significant interest recently. However, in the general case, existing efficient only achieved regret bound of O(T^{3/4}), which is worse than projection-based algorithms, where T number decision rounds. In this paper, we study special case lear...