Optimal pulse control of dynamic systems in the shock phase
Automation and Remote Control
Robust linear MIMO in the downlink: a worst-case optimization with ellipsoidal uncertainty regions
EURASIP Journal on Advances in Signal Processing
Cutting-set methods for robust convex optimization with pessimizing oracles
Optimization Methods & Software
Journal of Global Optimization
Robust collaborative-relay beamforming
IEEE Transactions on Signal Processing
Robust QoS-constrained optimization of downlink multiuser MISO systems
IEEE Transactions on Signal Processing
Removing redundant quadratic constraints
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Journal of Global Optimization
Some Equivalent Results with Yakubovich's $S$-Lemma
SIAM Journal on Control and Optimization
A Variational Approach to Copositive Matrices
SIAM Review
An iterative scheme for valid polynomial inequality generation in binary polynomial programming
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Second-Order Cone Relaxations for Binary Quadratic Polynomial Programs
SIAM Journal on Optimization
Theory and Applications of Robust Optimization
SIAM Review
On zero duality gap in nonconvex quadratic programming problems
Journal of Global Optimization
Eigenvalue techniques for convex objective, nonconvex optimization problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Journal of Global Optimization
A Kalman-Yakubovich-Popov-type lemma for systems with certain state-dependent constraints
Automatica (Journal of IFAC)
Worst-Case Value at Risk of Nonlinear Portfolios
Management Science
Semidefinite Programming-Based Method for Implementing Linear Fitting to Interval-Valued Data
International Journal of Fuzzy System Applications
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In this survey we review the many faces of the S-lemma, a result about the correctness of the S-procedure. The basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization, convex geometry, and linear algebra as well. These were all active research areas, but as there was little interaction between researchers in these different areas, their results remained mainly isolated. Here we give a unified analysis of the theory by providing three different proofs for the S-lemma and revealing hidden connections with various areas of mathematics. We prove some new duality results and present applications from control theory, error estimation, and computational geometry.