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Avtomat. i Telemekh., 2013, Issue 9, Pages 3–19 (Mi at6095)  

This article is cited in 29 scientific papers (total in 29 papers)

Nonlinear Systems

Lipschitz global optimization methods in control problems

D. E. Kvasovab, Ya. D. Sergeyevab

a Lobachevsky State University, Nizhni Novgorod, Russia
b Calabria University, Rende, Italy

Abstract: Many control problems involve the search for the global extremum in the space of states or the parameters of the system under study, which leads to the necessity of using effective methods of global finite-dimensional optimization. For this purpose use can be made of the geometric algorithms of Lipschitz global optimization, which are developed by the authors. A brief review of these algorithms is presented and they are compared with some algorithms of global search that are often used in technical practice. Numerical experiments are performed on a few known examples of applied multiextremal problems.

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English version:
Automation and Remote Control, 2013, 74:9, 1435–1448

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Presented by the member of Editorial Board: . . 

Received: 23.01.2013

Citation: D. E. Kvasov, Ya. D. Sergeyev, “Lipschitz global optimization methods in control problems”, Avtomat. i Telemekh., 2013, no. 9, 3–19; Autom. Remote Control, 74:9 (2013), 1435–1448

Citation in format AMSBIB
\by D.~E.~Kvasov, Ya.~D.~Sergeyev
\paper Lipschitz global optimization methods in control problems
\jour Avtomat. i Telemekh.
\yr 2013
\issue 9
\pages 3--19
\jour Autom. Remote Control
\yr 2013
\vol 74
\issue 9
\pages 1435--1448

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sergeyev Ya.D., Candelieri A., Kvasov D.E., Perego R., “Safe Global Optimization of Expensive Noisy Black-Box Functions in the Delta-Lipschitz Framework”, Soft Comput.  crossref  isi
    2. 90, no. 3, 2014, 791–794  crossref  mathscinet  zmath  isi  elib  scopus
    3. R. Paulavicius, Ya. D. Sergeyev, D. E. Kvasov, J. Zilinskas, “Globally-biased disimpl algorithm for expensive global optimization”, J. Glob. Optim., 59:2-3, SI (2014), 545–567  crossref  mathscinet  zmath  isi  elib  scopus
    4. D. Lera, Ya. D. Sergeyev, “Deterministic global optimization using space-filling curves and multiple estimates of lipschitz and holder constants”, Commun. Nonlinear Sci. Numer. Simul., 23:1-3 (2015), 328–342  crossref  mathscinet  zmath  isi  elib  scopus
    5. M. Shams, E. Rashedi, A. Hakimi, “Clustered-gravitational search algorithm and its application in parameter optimization of a low noise amplifier”, Appl. Math. Comput., 258 (2015), 436–453  crossref  mathscinet  zmath  isi  elib  scopus
    6. Ya. D. Sergeyev, M. S. Mukhametzhanov, D. E. Kvasov, D. Lera, “Derivative-free local tuning and local improvement techniques embedded in the univariate global optimization”, J. Optim. Theory Appl., 171:1 (2016), 186–208  crossref  mathscinet  zmath  isi  scopus
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    8. Ya. D. Sergeyev, D. E. Kvasov, M. S. Mukhametzhanov, “On the least-squares fitting of data by sinusoids”, Advances in Stochastic and Deterministic Global Optimization, Springer Optimization and Its Applications, 107, eds. P. Pardalos, A. Zhigljavsky, J. Zilinskas, Springler, 2016, 209–226  crossref  mathscinet  zmath  isi  scopus
    9. D. Lera, Ya. Sergeyev, “Remarks on global optimization using space-filling curves”, Numerical computations: theory and algorithms (NUMTA-2016), AIP Conf. Proc., 1776, eds. Y. Sergeyev, D. Kvasov, F. DellAccio, M. Mukhametzhanov, Amer. Inst. Phys., 2016, UNSP 060010  crossref  isi  scopus
    10. Zh. Jin, D. Y. Gao, “On modeling and global solutions for d.c. optimization problems by canonical duality theory”, Appl. Math. Comput., 296 (2017), 168–181  crossref  mathscinet  isi  elib  scopus
    11. J. W. Gillard, D. E. Kvasov, “Lipschitz optimization methods for fitting a sum of damped sinusoids to a series of observations”, Stat. Interface, 10:1 (2017), 59–70  crossref  mathscinet  zmath  isi  scopus
    12. Ya. D. Sergeyev, D. E. Kvasov, M. S. Mukhametzhanov, “Operational zones for comparing metaheuristic and deterministic one-dimensional global optimization algorithms”, Math. Comput. Simul., 141:SI (2017), 96–109  crossref  mathscinet  isi  scopus
    13. R. Paulavicius, L. Chiter, J. Zilinskas, “Global optimization based on bisection of rectangles, function values at diagonals, and a set of Lipschitz constants”, J. Glob. Optim., 71:1, SI (2018), 5–20  crossref  mathscinet  zmath  isi  scopus
    14. D. Lera, Ya. D. Sergeyev, “Gosh: derivative-free global optimization using multi-dimensional space-filling curves”, J. Glob. Optim., 71:1, SI (2018), 193–211  crossref  mathscinet  zmath  isi  scopus
    15. D. E. Kvasov, M. S. Mukhametzhanov, “Metaheuristic vs. Deterministic global optimization algorithms: the univariate case”, Appl. Math. Comput., 318 (2018), 245–259  crossref  mathscinet  isi  scopus
    16. V. Grishagin, R. Israfilov, Ya. Sergeyev, “Convergence conditions and numerical comparison of global optimization methods based on dimensionality reduction schemes”, Appl. Math. Comput., 318 (2018), 270–280  crossref  mathscinet  isi  scopus
    17. Sun Zh., Dawande M., Janakiraman G., Mookerjee V., “Data-Driven Decisions For Problems With An Unspecified Objective Function”, INFORMS J. Comput., 31:1 (2019), 2–20  crossref  isi  scopus
    18. Apinantanakon W., Pattanakitsiri S., Uttamaphant P., “The Cooperation of Candidate Solutions Vortex Search For Numerical Function Optimization”, Recent Advances in Information and Communication Technology 2018, Advances in Intelligent Systems and Computing, 769, eds. Unger H., Sodsee S., Meesad P., Springer International Publishing Ag, 2019, 135–144  crossref  isi  scopus
    19. Chao K.-H., Hsieh Ch.-Ch., “Photovoltaic Module Array Global Maximum Power Tracking Combined With Artificial Bee Colony and Particle Swarm Optimization Algorithm”, Electronics, 8:6 (2019), 603  crossref  isi
    20. Caraffini F., Kononova A.V., “Structural Bias in Differential Evolution: a Preliminary Study”, AIP Conference Proceedings, 2070, eds. Emmerich M., Deutz A., Hille S., Sergeyev Y., Amer Inst Physics, 2019, 020005  crossref  isi
    21. Kumar A. Jain T., “Computation of Linear Quadratic Regulator Using Krotov Sufficient Conditions”, 2019 Fifth Indian Control Conference (Icc), IEEE, 2019, 365–370  isi
    22. Kumar A. Jain T., “Linear Quadratic Optimal Control Design: a Novel Approach Based on Krotov Conditions”, Math. Probl. Eng., 2019 (2019), 9490512  crossref  mathscinet  isi
    23. Schmidt M., Sirvent M., Wollner W., “A Decomposition Method For Minlps With Lipschitz Continuous Nonlinearities”, Math. Program., 178:1-2 (2019), 449–483  crossref  mathscinet  isi
    24. R. G. Strongin, V. P. Gergel', K. A. Barkalov, “Adaptive global optimization based on a block-recursive dimensionality reduction scheme”, Autom. Remote Control, 81:8 (2020), 1475–1485  mathnet  crossref  crossref  isi  elib  elib
    25. Kodnyanko V.A., “Two Algorithms For Global Optimization of One-Variable Functions Based on the Smallest Estimate Distances Between Extremes and Their Number”, Radio Electron. Comput. Sci. Control, 2020, no. 2, 36–43  crossref  isi
    26. Paulavicius R., Sergeyev Ya.D., Kvasov D.E., Zilinskas J., “Globally-Biased Birect Algorithm With Local Accelerators For Expensive Global Optimization”, Expert Syst. Appl., 144 (2020), 113052  crossref  isi  scopus
    27. Kumar A. Jain T., “Some Insights on Synthesizing Optimal Linear Quadratic Controllers Using Krotov Sufficient Conditions”, IEEE Control Syst. Lett., 4:2 (2020), 486–491  crossref  mathscinet  isi  scopus
    28. Sergeyev Ya.D., Nasso M.Ch., Mukhametzhanov M.S., Kvasov D.E., “Novel Local Tuning Techniques For Speeding Up One-Dimensional Algorithms in Expensive Global Optimization Using Lipschitz Derivatives”, J. Comput. Appl. Math., 383 (2021), 113134  crossref  mathscinet  isi  scopus
    29. Lera D., Posypkin M., Sergeyev Ya.D., “Space-Filling Curves For Numerical Approximation and Visualization of Solutions to Systems of Nonlinear Inequalities With Applications in Robotics”, Appl. Math. Comput., 390 (2021), 125660  crossref  mathscinet  isi
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