Zobrazeno 1 - 10
of 38
pro vyhledávání: '"90C22, 90C23"'
Autor:
Laurent, Monique, Slot, Lucas
In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex) optimization
Externí odkaz:
http://arxiv.org/abs/2408.04417
We initiate a systematic study of nonnegative polynomials $P$ such that $P^k$ is not a sum of squares for any odd $k\geq 1$, calling such $P$ \emph{stubborn}. We develop a new invariant of a real isolated zero of a nonnegative polynomial in the plane
Externí odkaz:
http://arxiv.org/abs/2407.21779
Autor:
Slot, Lucas, Wiedmer, Manuel
Let $\mathbf{X} \subseteq \mathbb{R}^n$ be a closed set, and consider the problem of computing the minimum $f_{\min}$ of a polynomial $f$ on $\mathbf{X}$. Given a measure $\mu$ supported on $\mathbf{X}$, Lasserre (SIAM J. Optim. 21(3), 2011) proposes
Externí odkaz:
http://arxiv.org/abs/2404.09710
In this paper, we study a class of nonsmooth fractional programs {\rm (FP, for short)} with SOS-convex semi-algebraic functions. Under suitable assumptions, we derive a strong duality result between the problem (FP) and its semidefinite programming (
Externí odkaz:
http://arxiv.org/abs/2401.16716
In 1995, Reznick showed an important variant of the obvious fact that any positive semidefinite (real) quadratic form is a sum of squares of linear forms: If a form (of arbitrary even degree) is positive definite then it becomes a sum of squares of f
Externí odkaz:
http://arxiv.org/abs/2310.12853
Autor:
Wang, Jie
This note proposes a new reformulation of complex semidefinite programs (SDPs) as real SDPs. As an application, we present an economical reformulation of complex SDP relaxations of complex polynomial optimization problems as real SDPs and derive some
Externí odkaz:
http://arxiv.org/abs/2307.11599
The Moment/Sum-of-squares hierarchy provides a way to compute the global minimizers of polynomial optimization problems (POP), at the cost of solving a sequence of increasingly large semidefinite programs (SDPs). We consider large-scale POPs, for whi
Externí odkaz:
http://arxiv.org/abs/2305.16122
The moment-sum-of-squares (moment-SOS) hierarchy is one of the most celebrated and widely applied methods for approximating the minimum of an n-variate polynomial over a feasible region defined by polynomial (in)equalities. A key feature of the hiera
Externí odkaz:
http://arxiv.org/abs/2305.14944
Autor:
Averkov, Gennadiy, Scheiderer, Claus
Consider the closed convex hull $K$ of a monomial curve given parametrically as $(t^{m_1},\ldots,t^{m_n})$, with the parameter $t$ varying in an interval $I$. We show, using constructive arguments, that $K$ admits a lifted semidefinite description by
Externí odkaz:
http://arxiv.org/abs/2303.03826
We investigate some graph parameters dealing with biindependent pairs $(A,B)$ in a bipartite graph $G=(V_1\cup V_2,E)$, i.e., pairs $(A,B)$ where $A\subseteq V_1$, $B\subseteq V_2$ and $A\cup B$ is independent. These parameters also allow to study bi
Externí odkaz:
http://arxiv.org/abs/2302.08886