Some results on convex spectral functions. I. (English) Zbl 1412.15013
Summary: 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 these properties are inherited from the properties of its corresponding convex function. These results have many applications in applied mathematics such as semi-definite programmings and engineering problems.
MSC:
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 49J52 | Nonsmooth analysis |
| 47A75 | Eigenvalue problems for linear operators |
References:
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