Zobrazeno 1 - 10
of 171
pro vyhledávání: '"Harris, Mitchell A."'
Autor:
Harris, Mitchell Tong
Some sum of squares (SOS) polynomials admit decomposition certificates, or positive semidefinite Gram matrices, with additional structure. In this work, we use the structure of Gram matrices to relate the representation theory of $SL(2)$ to $SO(2)$.
Externí odkaz:
http://arxiv.org/abs/2407.20200
Optimizing and certifying the positivity of polynomials are fundamental primitives across mathematics and engineering applications, from dynamical systems to operations research. However, solving these problems in practice requires large semidefinite
Externí odkaz:
http://arxiv.org/abs/2312.02146
We present an efficient framework for solving algebraically-constrained global non-convex polynomial optimization problems over subsets of the hypercube. We prove the existence of an equivalent nonlinear reformulation of such problems that possesses
Externí odkaz:
http://arxiv.org/abs/2311.02037
We develop a new kind of nonnegativity certificate for univariate polynomials on an interval. In many applications, nonnegative Bernstein coefficients are often used as a simple way of certifying polynomial nonnegativity. Our proposed condition is in
Externí odkaz:
http://arxiv.org/abs/2309.10675
We study the problem of locating fire suppression resources in a burning landscape in order to minimise the total area burned. The landscape is modelled as a directed graph, with nodes representing regions of the landscape, and arcs representing adja
Externí odkaz:
http://arxiv.org/abs/2209.01371
Operations research practitioners frequently want to model complicated functions that are are difficult to encode in their underlying optimisation framework. A common approach is to solve an approximate model, and to use a simulation to evaluate the
Externí odkaz:
http://arxiv.org/abs/2107.08390
Autor:
Harris, Mitchell, Kalinowski, Thomas
We study the convex hull of the graph of a quadratic function $f(\mathbf{x})=\sum_{ij\in E}x_ix_j$, where the sum is over the edge set of a graph $G$ with vertex set $\{1,\dots,n\}$. Using an approach proposed by Gupte et al. (Discrete Optimization $
Externí odkaz:
http://arxiv.org/abs/2007.05656
Publikováno v:
In Computers and Operations Research December 2023 160
Autor:
Harris, Mitchell A.
The unit distance embeddability of a graph, like planarity, involves a mix of constraints that are combinatorial and geometric. We construct a unit distance embedding for $H-e$ in the hope that it will lead to an embedding for $H$. We then investigat
Externí odkaz:
http://arxiv.org/abs/0711.1157
We investigate the enumeration of varieties of boolean theories related to Horn clauses. We describe a number of combinatorial equivalences among different characterizations and calculate the number of different theories in $n$ variables for slightly
Externí odkaz:
http://arxiv.org/abs/cs/0610054