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세미나/워크샵 게시글의 상세 화면
제목 160830_11:00_Newton polyhedra, non-degeneracy conditions, and polynomial optimization
분류 세미나
작성자 빅데이터수리해석양성사업단 등록일 2016-08-28 조회수 473

아래와 같이 빅데이터 관련 특강을 개최하오니 많은 참석 부탁드립니다.


일시: 8월 30일 화요일 오전 11시~12시


장소: 32356A


연사:  Pham Tien Son




+ The first talk:

Title: Newton polyhedra, non-degeneracy conditions, and polynomial optimization

Abstract: In this talk we would like to define the class of generic polynomial optimization problems, that is, a class of polynomial optimization problems with ``nice properties'' (in terms of the objective function and the minimizers) and which contains ``almost all'' problems.

To identify generic problems we use the two important notions of Newton polyhedron and non-degeneracy conditions of a system of polynomials with respect to their Newton polyhedra.

Each set of polynomials is associated with some integer polytope in $\mathbb{R}^n,$ called the Newton polyhedron of the system. The set of all polynomials (or systems of polynomials) with fixed Newton polyhedra forms a finite dimensional space. In this space, a system is generic, if it satisfies the so-called non-degenerate condition (with respect to the Newton polyhedron). The set of generic systems forms an dense and open subset. Moreover this is an open set in the Zariski topology of the ambient space, or, equivalently, non generic systems are contained in the zero set of some polynomial. It turns out that this non-degenerate condition is very convenient for controlling behavior at infinity of the gradient of a function that we need to minimize. This fact is very important when the feasible set of a problem is not compact. In particular handling generic problems becomes much easier than handling non generic problems.

세미나/워크샵 게시판의 이전글 다음글
이전글 160830_15:00_Error bounds for parametric polynomial systems and applications.
다음글 160816_16:30_Introduction to deep learning