A Survey of the S-Lemma

By Imre Pólik, Tamás Terlaky. 2007

588 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

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Citations in the corpus

All Models are Wrong, but Many are Useful: Learning a Variable’s Importance by Studying an Entire Class of Prediction Models Simultaneously (2018, background): “This problem is well-studied, and is related to the trust region problem (Boyd and Vandenberghe, 2004; Pólik and Terlaky, 2007; Park and Boyd, 2017).”
Review on computational methods for Lyapunov functions (2015, methodology): “We refer the interested reader to the review paper P´olik and Terlaky 2007 [193] and let a simple example suﬃce to clarify its use.”
Distributionally robust joint chance constraints with second-order moment information (2011, methodology): “We refer to Pólik and Terlaky [22] for a derivation and an in-depth survey of the S-lemma as well as a review of the Farkas Lemma.”
Kalman-Popov-Yakubovich lemma and the S-procedure: A historical essay (2006, background): “A wide range of issues concerned with the S-procedure is discussed in the reviews [96, 97].”
All Models are Wrong but many are Useful: Variable Importance for Black-Box, Proprietary, or Misspecified Prediction Models, using Model Class Reliance (2018, background): “This problem is well studied, and is related to the trust region problem (Boyd and Vandenberghe, 2004; Pólik and Terlaky, 2007; Park and Boyd, 2017).”
Data-driven chance constrained stochastic program (2015, methodology): “g, Yakubovich [38] and Pólik and Terlaky [26]) and provides a general technique for handling DCCs with moment informations.”
From Noisy Data to Feedback Controllers: Nonconservative Design via a Matrix S-Lemma (2020, methodology): “First proven by Yakubovich [1], the S-lemma is a classical result in control theory and optimization [2].”
A Survey of Linear Parameter-Varying Control Applications Validated by Experiments or High-Fidelity Simulations (2015, unknown): “Historical surveys of the S-procedure can be found in [49] and [50].”
Theory and Applications of Robust Optimization (2010, background): “This is related to the so-called S -lemma (or S -procedure) in control (e.g., Boyd et al. [40], P´olik and Terlaky [119]): The S -lemma essentially gives the boundary between what we can solve exactly, and where solving the subproblem becomes diﬃcult.”
Distributionally Robust Optimization: A Review (2019, unknown): “[237] I.”
Robust Optimization (2021, background): “Yakubovich in 1971; for a comprehensive “optimization-oriented” survey of the related issues, see [70].”