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Found 12 papers, 6 papers with code
Local Lipschitz Constant Computation of ReLU-FNNs: Upper Bound Computation with Exactness Verification
By following a standard procedure using multipliers that capture the behavior of ReLUs, we first reduce the upper bound computation problem of the local Lipschitz constant into a semidefinite programming problem (SDP).
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).
Sparse Polynomial Optimization: Theory and Practice
Fortunately, for many applications, we can look at the problem in the eyes and exploit the inherent data structure arising from the cost and constraints describing the problem, for instance sparsity or symmetries.
Stability Analysis of Recurrent Neural Networks by IQC with Copositive Mutipliers
To get around this difficulty, we loosen the standard positive semidefinite cone to the copositive cone, and employ copositive multipliers to capture the nonnegativity properties.
The Constant Trace Property in Noncommutative Optimization
In this article, we show that each semidefinite relaxation of a ball-constrained noncommutative polynomial optimization problem can be cast as a semidefinite program with a constant trace matrix variable.
Optimization and Control
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
Minimizing rational functions: a hierarchy of approximations via pushforward measures
This paper is concerned with minimizing a sum of rational functions over a compact set of high-dimension.
Optimization and Control
Optimization over trace polynomials
Motivated by recent progress in quantum information theory, this article aims at optimizing trace polynomials, i. e., polynomials in noncommuting variables and traces of their products.
Mathematical Physics Functional Analysis Mathematical Physics Optimization and Control 46N50, 90C22, 47N10, 13J30
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
