A wide range of problems arising in practical applications can be formulated as Mixed-
Integer Nonlinear Programs (MINLPs). For the case in which the objective and constraint …

We prove that multilinear (tensor) analogues of many efficiently computable problems in
numerical linear algebra are NP-hard. Our list includes: determining the feasibility of a …

In recent years, optimization theory has been greatly impacted by the advent of sum of
squares (SOS) optimization. The reliance of this technique on large-scale semidefinite …

We introduce a novel representation of structured polynomial ideals, which we refer to as
chordal networks. The sparsity structure of a polynomial system is often described by a …

Systems of polynomial equations with coefficients over a field K can be used to concisely
model combinatorial problems. In this way, a combinatorial problem is feasible (eg, a graph …

Many hard combinatorial problems can be modeled by a system of polynomial equations. N.
Alon coined the term polynomial method to describe the use of nonlinear polynomials when …

Amoebas and coamoebas are the logarithmic images of algebraic varieties and the images
of algebraic varieties under the arg-map, respectively. We present new techniques for …

Abstract The field of Mathematical Programming offers a range of tools and algorithms to
solve optimization problems. Software based on these ideas is used in many application …

We consider a well-known family of polynomial ideals encoding the problem of graph-k-
colorability. Our paper describes how the inherent combinatorial structure of the ideals …

Abstract Systems of polynomial equations over an algebraically-closed field [special
characters omitted] can be used to concisely represent combinatorial decision problems. In …