컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0231 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | (AM) Applied Mathematics(including AI, Data Science) (AM) |
| 발표시간(Time) | 20th-D-13:00 -- 13:20 |
| 영문제목 (Title(Eng.)) |
Commutation principles for nonsmooth variational problems on Euclidean Jordan algebras |
| 저자(Author(s)) |
Juyoung Jeong1, David Sossa2 Changwon National University1, Universidad de O'Higgins2 |
| 초록본문(Abstract) | The commutation principle proved by Ramirez, Seeger, and Sossa in the setting of Euclidean Jordan algebras says that for a Frechet differentiable function $\Theta$ and a spectral function $F$, any local minimizer or maxmimizer $a$ of $\Theta+F$ over a spectral set $\mathcal{E}$ operator commutes with the gradient of $\Theta$ at $a$. In this paper, we improve this commutation principle by allowing $\Theta$ to be nonsmooth with mild regularity assumptions over it. For example, for the case of local minimizer, we show that $a$ operator commutes with some element of the limiting (Mordukhovich) subdifferential of $\Theta$ at $a$ provided that $\Theta$ is subdifferentially regular at $a$ satisfying a qualification condition. For the case of local maximizer, we prove that $a$ operator commutes with each element of the (Fenchel) subdifferential of $\Theta$ at $a$ whenever this subdifferential is nonempty. As an application, we characterize the local optimizers of shifted strictly convex spectral functions and norms over automorphism invariant sets. |
| 분류기호 (MSC number(s)) |
17C99, 17C30, 49J52, 90C56, 90C99 |
| 키워드(Keyword(s)) | Euclidean Jordan algebra, automorphism invariance, commutation principle, nonsmooth analysis, strictly convex norm |
| 강연 형태 (Language of Session (Talk)) |
Korean |