Related papers: Sum-of-Squares Polynomial Flow
In this paper we show that Sum-of-Squares optimization can be used to find optimal semialgebraic representations of sets. These sets may be explicitly defined, as in the case of discrete points or unions of sets; or implicitly defined, as…
Semidefinite and sum-of-squares (SOS) optimization are fundamental computational tools in many areas, including linear and nonlinear systems theory. However, the scale of problems that can be addressed reliably and efficiently is still…
We present a new data structure for representation of polynomial variables in the parsing of sum-of-squares (SOS) programs. In SOS programs, the variables $s(x;Q)$ are polynomial in the independent variables $x$, but linear in the decision…
Submodular functions can be exactly minimized in polynomial time, and the special case that graph cuts solve with max flow \cite{KZ:PAMI04} has had significant impact in computer vision \cite{BVZ:PAMI01,Kwatra:SIGGRAPH03,Rother:GrabCut04}.…
We provide a new algebraic technique to solve the sequential flow problem in polynomial space. The task is to maximise the flow through a graph where edge capacities can be changed over time by choosing a sequence of capacity labelings from…
The release of SOSTOOLS v4.00 comes as we approach the 20th anniversary of the original release of SOSTOOLS v1.00 back in April, 2002. SOSTOOLS was originally envisioned as a flexible tool for parsing and solving polynomial optimization…
We develop a general framework to significantly reduce the degree of sum-of-squares proofs by introducing new variables. To illustrate the power of this framework, we use it to speed up previous algorithms based on sum-of-squares for two…
In this article, we are interested in developing polynomial decomposition techniques based on sums-of-squares (SOS), namely the difference-of-sums-of-squares (D-SOS) and the difference-of-convex-sums-of-squares (DC-SOS). In particular, the…
We provide an asymptotically tight, computationally efficient approximation of the joint spectral radius of a set of matrices using sum of squares (SOS) programming. The approach is based on a search for an SOS polynomial that proves…
We introduce the notion of $t$-sum of squares (sos) submodularity, which is a hierarchy, indexed by $t$, of sufficient algebraic conditions for certifying submodularity of set functions. We show that, for fixed $t$, each level of the…
We suggest a new computer-assisted approach to the development of turbulence theory. It allows one to impose lower and upper bounds on correlation functions using sum-of-squares polynomials. We demonstrate it on the minimal cascade model of…
We present a hierarchy of semidefinite programs (SDPs) for the problem of fitting a shape-constrained (multivariate) polynomial to noisy evaluations of an unknown shape-constrained function. These shape constraints include convexity or…
Self-organizing maps (SOMs) are a technique that has been used with high-dimensional data vectors to develop an archetypal set of states (nodes) that span, in some sense, the high-dimensional space. Noteworthy applications include weather…
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…
In this paper, we propose a general sparse decomposition of dynamical systems provided that the vector field and constraint set possess certain sparse structures, which we call subsystems. This notion is based on causal dependence in the…
We present a faster interior-point method for optimizing sum-of-squares (SOS) polynomials, which are a central tool in polynomial optimization and capture convex programming in the Lasserre hierarchy. Let $p = \sum_i q^2_i$ be an…
The Gromov-Wasserstein (GW) problem is an extension of the classical optimal transport problem to settings where the source and target distributions reside in incomparable spaces, and for which a cost function that attributes the price of…
Normalizing flows are a powerful tool to create flexible probability distributions with a wide range of potential applications in cosmology. Here we are studying normalizing flows which represent cosmological observables at field level,…
The moment-sum of squares hierarchy by Lasserre has become an established technique for solving polynomial optimization problems. It provides a monotonically increasing series of tight bounds, but has well-known scalability limitations. For…
This work presents a computationally efficient approach to data-driven robust contracting controller synthesis for polynomial control-affine systems based on a sum-of-squares program. In particular, we consider the case in which a system…