Parabolic regularity in geometric variational analysis
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- by Ashkan Mohammadi, Boris S. Mordukhovich and M. Ebrahim Sarabi PDF
- Trans. Amer. Math. Soc. 374 (2021), 1711-1763 Request permission
Abstract:
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in variational analysis for more than two decades while being largely underinvestigated. We discover here that parabolic regularity is the key to derive new calculus rules and computation formulas for major second-order generalized differential constructions of variational analysis in connection with some properties of sets that go back to classical differential geometry and geometric measure theory. The established results of second-order variational analysis and generalized differentiation, being married to the developed calculus of parabolic regularity, allow us to obtain novel applications to both qualitative and quantitative/numerical aspects of constrained optimization including second-order optimality conditions, augmented Lagrangians, etc. under weak constraint qualifications.References
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Additional Information
- Ashkan Mohammadi
- Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
- ORCID: 0000-0002-3445-2406
- Email: ashkan.mohammadi@wayne.edu
- Boris S. Mordukhovich
- Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
- MR Author ID: 215154
- ORCID: 0000-0002-3445-2406
- Email: boris@math.wayne.edu
- M. Ebrahim Sarabi
- Affiliation: Department of Mathematics, Miami University, Oxford, Ohio 45065
- MR Author ID: 842219
- Email: sarabim@miamioh.edu
- Received by editor(s): September 2, 2019
- Received by editor(s) in revised form: June 15, 2020, and June 17, 2020
- Published electronically: December 18, 2020
- Additional Notes: The research of the first author was partly supported by the National Science Foundation under grant DMS-1808978 and by the U.S. Air Force Office of Scientific Research under grant #15RT0462.
The research of the second author was partly supported by the National Science Foundation under grants DMS-1512846 and DMS-1808978, by the U.S. Air Force Office of Scientific Research under grant #15RT0462, and by the Australian Research Council Discovery Project DP-190100555. - © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 1711-1763
- MSC (2020): Primary 90C31, 65K99, 49J52, 49J53
- DOI: https://doi.org/10.1090/tran/8253
- MathSciNet review: 4216722