Research

My research interests lie in the areas of optimization, variational analysis, and their applications into numerical algorithms.

Grants

My research is partially supported by the U.S. National Science Foundation (NSF) under the grant DMS 2108546 (August 2021-August 2024). If you are a graduate or an undergraduate student at Miami University with strong background in real analysis and would like to begin doing research in the area of optimization and variational analysis, you can send your request to sarabim@miamioh.edu. If you are outside of USA and are interested in pursuing research in optimization and variational analysis, you can apply for our graduate program using this link.

For the fall 2023, I am looking for a graduate student to study and conduct research in variational analysis under my direction. If you are interested in this position, you can email me. The minimum requirements for this position are:

  • You must be a US citizen;
  • You should have a strong background in real analysis;
  • This is a research position with no teaching responsibility, funded by NSF, and so you should be willing to spend a lot time to read and learn new topics.

Publication

  1. Role of Subgradients in Variational Analysis of Polyhedral Functions, preprint. (with W. Jung and N.T.V Hang).
  2. Local Convergence Analysis of Augmented Lagrangian Methods for Piecewise Linear-Quadratic Composite Optimization Problems, to appear in SIAM J. Optim. (2021), preprint. (with N.T.V Hang).
  3. Primal superlinear convergence of SQP methods in piecewise linear-quadratic composite optimization,  to appear in Set-Valued Var. Anal. (2021), preprint.
  4. Generalized Newton algorithms for tilt-stable minimizers in nonsmooth optimization,  SIAM J. Optim. 31 (2021), 1184–1214, preprint. (with B. S. Mordukhovich)
  5. Augmented Lagrangian method for second-order conic programs under second-order sufficiency,  preprint. (with N.T.V Hang and B. S. Mordukhovich)
  6. Twice epi-differentiability of extended-real-valued functions with applications in composite optimizationSIAM J. Optim. 30 (2020), 2379–2409, preprint. (with A. Mohammadi)
  7. Stability of KKT systems and superlinear convergence of the SQP method under parabolic regularity, J. Optim. Theory Appl., 186 (2020), 731-758, preprint. (with A. Mohammadi, B. S. Mordukhovich)
  8. Parabolic Regularity in Geometric Variational Analysis, Trans. Amer. Soc. 374 (2021), 1711–1763, preprint. (with A. Mohammadi, B. S. Mordukhovich)
  9. Variational Analysis of Composite Models with Applications to Continuous Optimizationto appear in Math. Oper. Res., preprint. (with A. Mohammadi, B. S. Mordukhovich)
  10. Criticality of Lagrange Multipliers in Extended Nonlinear OptimizationOptimization 70 (2021), 511-544, preprint. (with H. Do, B. S. Mordukhovich)
  11. Criticality of Lagrange Multipliers in Variational SystemsSIAM J. Optim. 29 (2019), 1524–1557. (with B. S. Mordukhovich)
  12. Second-Order Analysis in Second-Order Cone ProgrammingMath. Program. 180 (2020), 75–116. (with N.T.V Hang and B. S. Mordukhovich)
  13. Critical Multipliers in Variational Systems via Second-Order Generalized Differentiation, Math. Program. 169 (2018), 605–648, (pdf). (with B. S. Mordukhovich)
  14. Stability Analysis for Composite Optimization Problems and Parametric Variational SystemsJ. Optim. Theory Appl., 172 (2), 554-577 preprint. (with B. S. Mordukhovich)
  15. Generalized differentiation of piecewise linear functions in second-order variational analysis, Nonlinear Anal. 132 (2016), 240-273.preprint. (with B. S. Mordukhovich)
  16. Second-order analysis of piecewise linear functions with applications to optimization and stability, J. Optim. Theory Appl. (2016), 1-23. preprint. (with B. S. Mordukhovich)
  17. Variational analysis and full stability of optimal solutions to constrained and minimax problems, Nonlinear Anal. 121 (2015), 36-53. preprint. (with B. S. Mordukhovich)
  18. Full stability in second-order cone programming, SIAM J. Optim. 24 (2014), no. 4, 1581-1613. (with B. S. Mordukhovich, J. V. Outrata)
  19. Characterizations of full stability in constrained optimization, SIAM J. Optim. 23 (2013), no. 3, 1810-1849. (with B. S. Mordukhovich, R. T. Rockafellar)
  20. Existence of solutions in variational relation problems without convexity, J. Math. Anal. Appl. 364 (2010), no. 2,544-555. (with D. T. Luc, A. Soubeyran)
  21. Pseudo-Hessian and Taylor’s expansion for vectorvalued functions, Nonlinear Anal. 72 (2010), no. 3-4, 1938-1948. (with E. Babolian)
  22. Revisiting the gap function of a multicriteria optimization problem, Int. J. Comput. Math. 86 (2009), no. 5, 860-863. (with M. Soleimani-damaneh)
  23. Taylor’s expansion for C^{1,1} functions in Asplund spaces, Nonlinear Anal. 71 (2009), no. 11, 5707-5711.
  24. Sufficient conditions for nonsmooth rinvexity, Numer. Funct. Anal. Optim. 29 (2008), no. 5-6, 674-686. (with M. Soleimani-damaneh)

Talks

  1. Joint Mathematics Meetings, Special Session on “Variational Analysis and Optimiza- tion,” Washington, D.C. (virtual), January 6-9, 2021.
  2. Joint Mathematics Meetings, Special Session on “Set-Valued and Fuzzy-Valued Anal- ysis with Applications,” Denver, CO, January 15-18, 2020.
  3. Sixth International Conference on Continuous Optimization (ICCOPT), the Weier- strass Institute for Applied Analysis and Stochastic, Berlin, Germany, August 3-8, 2019.
  4. International Workshop on Variational Analysis and Related Topics, Hanoi Pedagogical University 2, Vietnam, December 13-15, 2018.
  5. AMS Sectional Meeting, Special Session on “Set-Valued optimization and Variational Problems with Applications,” Portland State University, April 2018.
  6. Global Optimization Conference (GOC-2017), Texas A & M University, April 2017.
  7. Midwest Optimization Meeting, Department of Mathematics, Michigan State Univer- sity, October 2016.
  8. Joint Mathematics Meetings, Special Session on “Set-Valued optimization and Varia- tional Problems with Applications,” Seattle, WA, January 2016.
  9. Midwest Optimization Meeting, Department of Mathematics, Loyola University, CI, October 2015.
  10. 22nd International Symposium on Mathematical Programming, Special Session on “Variational Analysis in Nonsmooth Optimization,” Pittsburgh University, PA, July 2015.
  11. Midwest Optimization Meeting, Department of Mathematics, Loyola University, CI, October 2014.
  12. Michigan Mathematics Meetings, University of Michigan-Flint, MI, May 2014.
  13. Joint Mathematics Meetings, Special Session on “Set-Valued optimization and Varia- tional Problems with Applications,” Baltimore, MD, January 2014.
  14. Midwest Optimization Meeting, Department of Mathematics, Western Michigan Uni- versity, MI, October 2012.
  15. Optimization Seminar group, Avignon University, France, May 2009.

Editorial Membership

  1. Member of the editorial board of the Journal of Nonsmooth Analysis and Optimization since October 2019.
  2. Member of the editorial board of the Journal of the Journal of Optimization Theory and Applications since June 2020.

Conference Organization

  1. The 2018 Midwest Optimization Meetings , Miami University, OH (with Olga Brezhneva, Douglas Ward, and Stephen E. Wright).
  2. The 2020 Midwest Optimization Meetings , virtual (with B. Mordukhovich and H. Wolkowicz).