Representation of Non-negative Polynomials via the Kkt Ideals
نویسندگان
چکیده
This paper studies the representation of a non-negative polynomial f on a non-compact semi-algebraic set K modulo its KKT (Karush-KuhnTucker) ideal. Under the assumption that f satisfies the boundary Hessian conditions (BHC) at each zero of f in K; we show that f can be represented as a sum of squares (SOS) of real polynomials modulo its KKT ideal if f ≥ 0 on K.
منابع مشابه
Representations of positive polynomials on non-compact semialgebraic sets via KKT ideals
This paper studies the representation of a positive polynomial f(x) on a noncompact semialgebraic set S = {x ∈ R : g1(x) ≥ 0, · · · , gs(x) ≥ 0} modulo its KKT (Karush-KuhnTucker) ideal. Under the assumption that the minimum value of f(x) on S is attained at some KKT point, we show that f(x) can be represented as sum of squares (SOS) of polynomials modulo the KKT ideal if f(x) > 0 on S; further...
متن کاملRepresentations of Non-negative Polynomials via the Critical Ideals
This paper studies the representations of a non-negative polynomial f on a non-compact semi-algebraic set K modulo its critical ideal. Under the assumption that the semi-algebraic set K is regular and f satisfies the boundary Hessian conditions (BHC) at each zero of f in K. We show that f can be represented as a sum of squares (SOS) of real polynomials modulo its critical ideal if f ≥ 0 on K. P...
متن کاملON THE USE OF KULSHAMMER TYPE INVARIANTS IN REPRESENTATION THEORY
Since 2005 a new powerful invariant of an algebra has emerged using the earlier work of Horvath, Hethelyi, Kulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. It was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...
متن کاملImage Classification via Sparse Representation and Subspace Alignment
Image representation is a crucial problem in image processing where there exist many low-level representations of image, i.e., SIFT, HOG and so on. But there is a missing link across low-level and high-level semantic representations. In fact, traditional machine learning approaches, e.g., non-negative matrix factorization, sparse representation and principle component analysis are employed to d...
متن کاملPrimal strong co-ideals in semirings
In this paper, we introduce the notion of primal strong co-ideals and give some results involving them. It is shown thatsubtractive strong co-ideals are intersection of all primal strong co-ideals that contain them. Also we prove that the representation of strong co-ideals as reduced intersections of primal strong co-ideals is unique.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010