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Contemporary Mathematics. Fundamental Directions
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Contemporary Mathematics. Fundamental Directions, 2007, Volume 22, Pages 5–37 (Mi cmfd83)  

This article is cited in 83 scientific papers (total in 83 papers)

Approximation of Convex Sets by Polytopes

E. M. Bronshtein
References:
English version:
Journal of Mathematical Sciences, 2008, Volume 153, Issue 6, Pages 727–762
DOI: https://doi.org/10.1007/s10958-008-9144-x
Bibliographic databases:
UDC: 514.11
Language: Russian
Citation: E. M. Bronshtein, “Approximation of Convex Sets by Polytopes”, Geometry, CMFD, 22, PFUR, M., 2007, 5–37; Journal of Mathematical Sciences, 153:6 (2008), 727–762
Citation in format AMSBIB
\Bibitem{Bro07}
\by E.~M.~Bronshtein
\paper Approximation of Convex Sets by Polytopes
\inbook Geometry
\serial CMFD
\yr 2007
\vol 22
\pages 5--37
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd83}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336506}
\zmath{https://zbmath.org/?q=an:1161.52001}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 153
\issue 6
\pages 727--762
\crossref{https://doi.org/10.1007/s10958-008-9144-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-54249167871}
Linking options:
  • https://www.mathnet.ru/eng/cmfd83
  • https://www.mathnet.ru/eng/cmfd/v22/p5
  • This publication is cited in the following 83 articles:
    1. Gabriela Kováčová, Birgit Rudloff, “Approximations of unbounded convex projections and unbounded convex sets”, J Glob Optim, 2025  crossref
    2. Vladimir Lotoreichik, “Inequalities between Dirichlet and Neumann eigenvalues of the magnetic Laplacian”, Lett Math Phys, 115:1 (2025)  crossref
    3. Ravi Raushan, Debdas Ghosh, Yong Zhao, Zhou Wei, “A Method for Uncertain Linear Optimization Problems Through Polytopic Approximation of the Uncertainty Set”, J Optim Theory Appl, 205:1 (2025)  crossref
    4. Zahra Marvi, Francesco Bullo, Andrew G. Alleyne, “Control Barrier Proximal Dynamics: A Contraction Theoretic Approach for Safety Verification”, IEEE Control Syst. Lett., 8 (2024), 880  crossref
    5. Gehui Xu, Guanpu Chen, Zhaoyang Cheng, Yiguang Hong, Hongsheng Qi, “Consistency of Stackelberg and Nash Equilibria in Three-Player Leader-Follower Games”, IEEE Trans.Inform.Forensic Secur., 19 (2024), 5330  crossref
    6. Bryan Convens, Dominic Liao-McPherson, Kelly Merckaert, Bram Vanderborght, Marco M. Nicotra, “A Terminal State Feasibility Governor for Real-Time Nonlinear Model Predictive Control Over Arbitrary Horizons”, IEEE Trans. Contr. Syst. Technol., 32:4 (2024), 1341  crossref
    7. Shui Fu, Rui Wang, Wentao Tang, Xi‐Ming Sun, “Guaranteed Disturbance Compensation and Robust Fault Detection Based on Zonotopic Evaluation”, Intl J Robust & Nonlinear, 2024  crossref
    8. Anindya De, Shivam Nadimpalli, Rocco A. Servedio, 2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS), 2024, 1911  crossref
    9. Zahra Marvi, Francesco Bullo, Andrew G. Alleyne, “Robust and Exponential Stability in Barrier-Certified Systems via Contracting Piecewise Smooth Dynamics”, IEEE Control Syst. Lett., 8 (2024), 3279  crossref
    10. Gehui Xu, Guanpu Chen, Hongsheng Qi, “Algorithm Design and Approximation Analysis on Distributed Robust Game”, J Syst Sci Complex, 36:2 (2023), 480  crossref
    11. Gehui Xu, Guanpu Chen, Hongsheng Qi, Yiguang Hong, “Efficient Algorithm for Approximating Nash Equilibrium of Distributed Aggregative Games”, IEEE Trans. Cybern., 53:7 (2023), 4375  crossref
    12. Raffaele Iervolino, Roberto Ambrosino, “Stabilizing control design for state-dependent impulsive dynamical linear systems”, Automatica, 147 (2023), 110681  crossref
    13. Markus P. Müller, Andrew J. P. Garner, “Testing Quantum Theory by Generalizing Noncontextuality”, Phys. Rev. X, 13:4 (2023)  crossref
    14. Kinga Nagy, Viktor Vígh, “Best and Random Approximations with Generalized Disc–Polygons”, Discrete Comput Geom, 2023  crossref
    15. Raffaele Iervolino, Roberto Ambrosino, “Finite-time stabilization of state dependent impulsive dynamical linear systems”, Nonlinear Analysis: Hybrid Systems, 47 (2023), 101305  crossref
    16. Ignacio Sanchez, Christophe Louembet, Marcelo Actis, Alejandro H. Gonzalez, “Characterization and computation of control invariant sets for linear impulsive control systems”, Nonlinear Analysis: Hybrid Systems, 47 (2023), 101271  crossref
    17. Andreas Bluhm, Ion Nechita, Simon Schmidt, “Polytope compatibility—From quantum measurements to magic squares”, Journal of Mathematical Physics, 64:12 (2023)  crossref
    18. Siva Athreya, Purvi Gupta, D. Yogeshwaran, “Volume approximation of strongly C-convex domains by random polyhedra”, Advances in Mathematics, 432 (2023), 109243  crossref
    19. Michele Caprio, Sayan Mukherjee, “Ergodic theorems for dynamic imprecise probability kinematics”, International Journal of Approximate Reasoning, 152 (2023), 325  crossref
    20. Terrence Skibik, Dominic Liao-McPherson, Marco M. Nicotra, “A Terminal Set Feasibility Governor for Linear Model Predictive Control”, IEEE Trans. Automat. Contr., 68:8 (2023), 5089  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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