Polynomial solution to stabilization problem for multivariable sampled-data systems with time delay
Automation and Remote Control
A probabilistic analytic center cutting plane method for feasibility of uncertain LMIs
Automatica (Journal of IFAC)
Optimal Solutions for Sparse Principal Component Analysis
The Journal of Machine Learning Research
D-decomposition technique state-of-the-art
Automation and Remote Control
On Safe Tractable Approximations of Chance-Constrained Linear Matrix Inequalities
Mathematics of Operations Research
Exploiting sparsity in the sum-of-squares approximations to robust semidefinite programs
ACC'09 Proceedings of the 2009 conference on American Control Conference
The positive semidefinite Grothendieck problem with rank constraint
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Theory and Applications of Robust Optimization
SIAM Review
Ellipsoidal bounds for uncertain linear equations and dynamical systems
Automatica (Journal of IFAC)
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We present efficiently verifiable sufficient conditions for the validity of specific NP-hard semi-infinite systems of linear matrix inequalities (LMIs) arising from LMIs with uncertain data and demonstrate that these conditions are "tight" up to an absolute constant factor. In particular, we prove that given an $n\times n$ interval matrix ${\cal U}_\rho=\{A\mid\, |A_{ij}-A^*_{ij}|\leq\rho C_{ij}\}$, one can build a computable lower bound, accurate within the factor ${\pi\over 2}$, on the supremum of those $\rho$ for which all instances of ${\cal U}_\rho$ share a common quadratic Lyapunov function. We then obtain a similar result for the problem of quadratic Lyapunov stability synthesis. Finally, we apply our techniques to the problem of maximizing a homogeneous polynomial of degree 3 over the unit cube.