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Found 8 papers, 7 papers with code
Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization
We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery.
Finding unstable periodic orbits: a hybrid approach with polynomial optimization
We present a novel method to compute unstable periodic orbits (UPOs) that optimize the infinite-time average of a given quantity for polynomial ODE systems.
Dynamical Systems Optimization and Control Chaotic Dynamics
Sum-of-squares chordal decomposition of polynomial matrix inequalities
Third, we prove that if $P$ is positive definite on a compact semialgebraic set $\mathcal{K}=\{x:g_1(x)\geq 0,\ldots, g_m(x)\geq 0\}$ satisfying the Archimedean condition, then $P(x) = S_0(x) + g_1(x)S_1(x) + \cdots + g_m(x)S_m(x)$ for matrices $S_i(x)$ that are sums of sparse SOS matrices.
Optimization and Control Data Structures and Algorithms Systems and Control Systems and Control Algebraic Geometry
Sparse sum-of-squares (SOS) optimization: A bridge between DSOS/SDSOS and SOS optimization for sparse polynomials
Optimization over non-negative polynomials is fundamental for nonlinear systems analysis and control.
Optimization and Control Systems and Control
Decomposition and Completion of Sum-of-Squares Matrices
We show that a subset of sparse SOS matrices with chordal sparsity patterns can be equivalently decomposed into a sum of multiple SOS matrices that are nonzero only on a principal submatrix.
Optimization and Control Systems and Control
Chordal decomposition in operator-splitting methods for sparse semidefinite programs
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 semidefinite (PSD) constraints.
Optimization and Control
Fast ADMM for homogeneous self-dual embedding of sparse SDPs
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 pair of semidefinite programs (SDPs) with chordal sparsity.
Optimization and Control
Fast ADMM for Semidefinite Programs with Chordal Sparsity
We show that chordal decomposition can be applied to either the primal or the dual standard form of a sparse SDP, resulting in scaled versions of ADMM algorithms with the same computational cost.
Optimization and Control
