64 citations · 563 across the 39 of their papers we have counts for
18 papers · 1 filter
Optimizing bounds for energy-constrained optimal cooling problems in two dimensions
Pedro Blöss Braga, Giovanni Fantuzzi
We study optimal control problems for incompressible fluids in two-dimensional domains with a cold boundary and internal heat sources and sinks. Given a kinetic energy budget, meas…
Polyconvexity with Moments and Sums of Squares
Giovanni Fantuzzi, Didier Henrion, Martin Kru{ž}ík +2
A function of a matrix is polyconvex when it can be expressed as a convex function of the matrix minors. Polyconvexity is a regularity condition ensuring existence of minimizers in…
Global minimization of polynomial integral functionals
Giovanni Fantuzzi, Federico Fuentes
We describe a `discretize-then-relax' strategy to globally minimize integral functionals over functions in a Sobolev space subject to Dirichlet boundary conditions. The strateg…
Uncertainty propagation for nonlinear dynamics: A polynomial optimization approach
Francesca Covella, Giovanni Fantuzzi
We use Lyapunov-like functions and convex optimization to propagate uncertainty in the initial condition of nonlinear systems governed by ordinary differential equations. We consid…
Sharpness and non-sharpness of occupation measure bounds for integral variational problems
Giovanni Fantuzzi, Ian Tobasco
We analyze two recently proposed methods to establish a priori lower bounds on the minimum of general integral variational problems. The methods, which involve either `occupation m…
Verification of some functional inequalities via polynomial optimization
Giovanni Fantuzzi
Motivated by the application of Lyapunov methods to partial differential equations (PDEs), we study functional inequalities of the form where is…
Convex relaxations of integral variational problems: pointwise dual relaxation and sum-of-squares optimization
Alexander Chernyavsky, Jason J. Bramburger, Giovanni Fantuzzi +1
We present a method for finding lower bounds on the global infima of integral variational problems, wherein is minimized over functions $u\col…
Chordal and factor-width decompositions for scalable semidefinite and polynomial optimization
Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou
Chordal and factor-width decomposition methods for semidefinite programming and polynomial optimization have recently enabled the analysis and control of large-scale linear systems…
Sum-of-squares chordal decomposition of polynomial matrix inequalities
Yang Zheng, Giovanni Fantuzzi
We prove decomposition theorems for sparse positive (semi)definite polynomial matrices that can be viewed as sparsity-exploiting versions of the Hilbert--Artin, Reznick, Putinar, a…
Duality of convex relaxations for constrained variational problems
Giovanni Fantuzzi
We prove weak duality between two recent convex relaxation methods for bounding the optimal value of a constrained variational problem in which the objective is an integral functio…
Sparse sum-of-squares (SOS) optimization: A bridge between DSOS/SDSOS and SOS optimization for sparse polynomials
Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou
Optimization over non-negative polynomials is fundamental for nonlinear systems analysis and control. We investigate the relation between three tractable relaxations for optimizing…
Decomposition and Completion of Sum-of-Squares Matrices
Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou
This paper introduces a notion of decomposition and completion of sum-of-squares (SOS) matrices. We show that a subset of sparse SOS matrices with chordal sparsity patterns can be…
Fast ADMM for sum-of-squares programs using partial orthogonality
Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou
When sum-of-squares (SOS) programs are recast as semidefinite programs (SDPs) using the standard monomial basis, the constraint matrices in the SDP possess a structural property th…
Chordal decomposition in operator-splitting methods for sparse semidefinite programs
Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou +2
We employ chordal decomposition to reformulate a large and sparse semidefinite program (SDP), either in primal or dual standard form, into an equivalent SDP with smaller positive s…
Exploiting Sparsity in the Coefficient Matching Conditions in Sum-of-Squares Programming using ADMM
Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou
This paper introduces an efficient first-order method based on the alternating direction method of multipliers (ADMM) to solve semidefinite programs (SDPs) arising from sum-of-squa…
Fast ADMM for homogeneous self-dual embedding of sparse SDPs
Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou +2
We propose an efficient first-order method, based on the alternating direction method of multipliers (ADMM), to solve the homogeneous self-dual embedding problem for a primal-dual…
Fast ADMM for Semidefinite Programs with Chordal Sparsity
Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou +2
Many problems in control theory can be formulated as semidefinite programs (SDPs). For large-scale SDPs, it is important to exploit the inherent sparsity to improve the scalability…
Optimization with affine homogeneous quadratic integral inequality constraints
Giovanni Fantuzzi, Andrew Wynn, Paul Goulart +1
We introduce a new technique to optimize a linear cost function subject to a one-dimensional affine homogeneous quadratic integral inequality, i.e., the requirement that a homogene…