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Found 10 papers, 6 papers with code
Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant
We consider polynomial optimization problems (POP) on a semialgebraic set contained in the nonnegative orthant (every POP on a compact set can be put in this format by a simple translation of the origin).
A Sublevel Moment-SOS Hierarchy for Polynomial Optimization
We introduce a sublevel Moment-SOS hierarchy where each SDP relaxation can be viewed as an intermediate (or interpolation) between the d-th and (d+1)-th order SDP relaxations of the Moment-SOS hierarchy (dense or sparse version).
Combinatorial Optimization
Optimization and Control
Chordal-TSSOS: a moment-SOS hierarchy that exploits term sparsity with chordal extension
The novelty and distinguishing feature of such relaxations is to obtain quasi block-diagonal matrices obtained in an iterative procedure that performs chordal extension of certain adjacency graphs.
Optimization and Control 14P10, 90C25, 12D15, 12Y05
Semialgebraic Optimization for Lipschitz Constants of ReLU Networks
The Lipschitz constant of a network plays an important role in many applications of deep learning, such as robustness certification and Wasserstein Generative Adversarial Network.
TSSOS: A Moment-SOS hierarchy that exploits term sparsity
This paper is concerned with polynomial optimization problems.
Optimization and Control
Positivity certificates and polynomial optimization on non-compact semialgebraic sets
As a consequence, it allows one to define a hierarchy of semidefinite relaxations for a general polynomial optimization problem.
Optimization and Control
Data analysis from empirical moments and the Christoffel function
Spectral features of the empirical moment matrix constitute a resourceful tool for unveiling properties of a cloud of points, among which, density, support and latent structures.
Approximate Optimal Designs for Multivariate Polynomial Regression
We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces.
Statistics Theory Information Theory Information Theory Numerical Analysis Computation Methodology Statistics Theory 62K05, 90C25 (Primary) 41A10, 49M29, 90C90, 15A15 (secondary)
The empirical Christoffel function with applications in data analysis
Secondly, we provide a consistency result which relates the empirical Christoffel function and its population counterpart in the limit of large samples.
Sorting out typicality with the inverse moment matrix SOS polynomial
In fact, this SOS polynomial is directly related to orthogonal polynomials and the Christoffel function.
