Abstract
Abstract Text
Similar content being viewed by others
References
Attouch H, Buttazzo G, Michaille G (2014) Variational analysis in Sobolev and BV spaces, 2nd edn. SIAM, Philadelphia
Bonnans JF, Shapiro A (2000) Perturbation analysis of optimization problems. Springer, New York
Borwein JM, Zhu QJ (2005) Techniques of variational analysis. Springer, New York
Clarke FH (1975) Generalized gradients and applications. Trans Amer Math Soc 205:247–262
Clarke FH (1983) Optimization and nonsmooth analysis. Wiley-Interscience, New York
Dontchev AL, Rockafellar RT (2014) Implicit functions and solution mappings: a view from variational analysis, 2nd edn. Springer, New York
Ioffe AD (2017) Variational analysis of regular mappings: theory and applications. Springer, Cham
Klatte D, Kummer B (2002) Nonsmooth equations in optimization: regularity, calculus, methods and applications. Kluwer, Boston
Levy AB, Poliquin RA, Rockafellar RT (2000) Stability of locally optimal solutions. SIAM J Optim 10:580–604
Mohammadi A, Mordukhovich BS, Sarabi ME (2021) Parabolic regularity in geometric variational analysis. Trans Am Math Soc 374:1711–1763
Mordukhovich BS (1976) Maximum principle in problems of time optimal control with nonsmooth constraints. J Appl Math Mech 40:960–969
Mordukhovich BS (1992) Sensitivity analysis in nonsmooth optimization. SIAM Proc Appl Math 58:32–46. Field DA, Komkov V (eds) Theoretical aspects of industrial design
Mordukhovich BS (1993) Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions. Trans Am Math Soc 340:1–35
Mordukhovich BS (2006) Variational analysis and generalized differentiation, I: Basic theory, II: Applications. Springer, Berlin
Mordukhovich BS (2018) Variational analysis and applications. Springer, Cham
Mordukhovich BS, Rockafellar RT (2012) Second-order subdifferential calculus with applications to tilt stability in optimization. SIAM J Optim 22:953–986
Mordukhovich BS, Sarabi ME (2021) Generalized Newton algorithms for tilt-stable minimizers in nonsmooth optimization. SIAM J Optim 31:1184–1214
Penot J-P (2013) Calculus without derivatives. Springer, New York
Rockafellar RT, Wets RJ-B (1998) Variational analysis. Springer, Berlin
Vinter RB (2000) Optimal control. Birkhäuser, Boston
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 Springer Nature Switzerland AG
About this entry
Cite this entry
Mordukhovich, B.S. (2023). Variational Analysis. In: Pardalos, P.M., Prokopyev, O.A. (eds) Encyclopedia of Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-54621-2_734-1
Download citation
DOI: https://doi.org/10.1007/978-3-030-54621-2_734-1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-54621-2
Online ISBN: 978-3-030-54621-2
eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering