6 citations · 7 across the 11 of their papers we have counts for
11 papers
Osculating Geometry and Higher-Order Distance Loci
Sandra Di Rocco, Kemal Rose, Luca Sodomaco
We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Eucli…
Computing positive tropical varieties and lower bounds on the number of positive roots
Kemal Rose, Máté L. Telek
We present two effective tools for computing the positive tropicalization of algebraic varieties. First, we outline conditions under which the initial ideal can be used to compute…
The polyhedral type of a polynomial map on the plane
Boulos El Hilany, Kemal Rose
Two continuous maps are said to be topologically equivalent if there exist homeomorphisms satisfying $ψ\circ…
The algebraic degree of sparse polynomial optimization
Julia Lindberg, Leonid Monin, Kemal Rose
We study a broad class of polynomial optimization problems whose constraints and objective functions exhibit sparsity patterns. We give two characterizations of the number of criti…
Tropical Implicitization Revisited
Kemal Rose, Bernd Sturmfels, Simon Telen
Tropical implicitization means computing the tropicalization of a unirational variety from its parametrization. In the case of a hypersurface, this amounts to finding the Newton po…
A polyhedral homotopy algorithm for computing critical points of polynomial programs
Julia Lindberg, Leonid Monin, Kemal Rose
In this paper we propose a method that uses Lagrange multipliers and numerical algebraic geometry to find all critical points, and therefore globally solve, polynomial optimization…
Algebraic optimization of sequential decision problems
Mareike Dressler, Marina Garrote-López, Guido Montúfar +2
We study the optimization of the expected long-term reward in finite partially observable Markov decision processes over the set of stationary stochastic policies. In the case of d…
Multi-Degrees in Polynomial Optimization
Kemal Rose
We study structured optimization problems with polynomial objective function and polynomial equality constraints. The structure comes from a multi-grading on the polynomial ring in…
Toric non-Gorenstein loci
Kemal Rose
We describe the non-Gorenstein loci of normal toric varieties. In the case of Hibi rings a combinatorial description is provided in terms of the underlying partially ordered set. A…
Lines on -adic and real cubic surfaces
Rida Ait El Manssour, Yassine El Maazouz, Enis Kaya +1
We study lines on smooth cubic surfaces over the field of -adic numbers, from a theoretical and computational point of view. Segre showed that the possible counts of such lines…
Certifying zeros of polynomial systems using interval arithmetic
Paul Breiding, Kemal Rose, Sascha Timme
We establish interval arithmetic as a practical tool for certification in numerical algebraic geometry. Our software HomotopyContinuation.jl now has a built-in function certify, wh…