9 citations · 43 across the 12 of their papers we have counts for
4 papers · 1 filter
Sequential sum-of-squares programming for analysis of nonlinear systems
Torbjørn Cunis, Benoît Legat
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems eff…
Flexible Differentiable Optimization via Model Transformations
Mathieu Besançon, Joaquim Dias Garcia, Benoît Legat +1
We introduce DiffOpt.jl, a Julia library to differentiate through the solution of optimization problems with respect to arbitrary parameters present in the objective and/or constra…
JuMP 1.0: Recent improvements to a modeling language for mathematical optimization
Miles Lubin, Oscar Dowson, Joaquim Dias Garcia +3
JuMP is an algebraic modeling language embedded in the Julia programming language. JuMP allows users to model optimization problems of a variety of kinds, including linear programm…
Low-Rank Univariate Sum of Squares Has No Spurious Local Minima
Benoît Legat, Chenyang Yuan, Pablo A. Parrilo
We study the problem of decomposing a polynomial into a sum of squares by minimizing a quadratically penalized objective $f_p(\mathbf{u}) = \left\lVert \sum_{i=1}^r u_i^2 -…