Books

• Shikhman, Vladimir ; Müller, David. Mathematical Foundations of Big Data Analytics, Springer Gabler: Berlin, 2021. ISBN 978-3-662-62520-0. 230 p.
• Shikhman, Vladimir. Mathematik für Wirtschaftswissenschaftler: In 60 fachübergreifenden Vorlesungen präsentiert, Springer Gabler: Wiesbaden, 2019. ISBN 978-3-658-24542-9. 472 p.
• Shikhman, Vladimir. Topological Aspects of Nonsmooth Optimization (Nonconvex Optimization and Its Applications; 64), Springer: New York, 2012. ISBN 9781461418979. 193 p.

Preprints

• Lampariello, Lorenzo ; Sagratella, Simone ; Sasso, Valerio Guiseppe ; Shikhman, Vladimir. Scalarization via utility functions in multi-objective optimization. 30 pages (2024). arXiv:2401.13831
• Lämmel, Sebastian ; Shikhman, Vladimir. Shannon's comparison of channels characterized by optimal decision making. 19 pages (2019). arXiv:1906.07041

Papers

2024:

• Lämmel, Sebastian ; Shikhman, Vladimir. Extended convergence analysis of the Scholtes-type regularization for cardinality-constrained optimization problems. In: Mathematical Programming, online first. doi.org/10.1007/s10107-024-02082-3
• Lämmel, Sebastian ; Shikhman, Vladimir. Global aspects of the continuous reformulation for cardinality-constrained optimization problems. In: Optimization, online first. doi.org/10.1080/02331934.2023.2249014

2023:

• Lämmel, Sebastian ; Shikhman, Vladimir. Critical point theory for sparse recovery. In: Optimization (2023), Vol. 72, p. 521-549 (2023). doi.org/10.1080/02331934.2021.1981317
• Kungurtsev, Vyacheslav ; Shikhman, Vladimir. Regularized quasi-monotone method for stochastic optimization. In: Optimization Letters, Vol. 17, p. 1215-1228 (2023). doi.org/10.1007/s11590-022-01931-4
• Lämmel, Sebastian ; Shikhman, Vladimir. Optimality conditions for mathematical programs with orthogonality type constraints. In: Set-Valued and Variational Analysis (2023), Vol. 31, Article number: 9. doi.org/10.1007/s11228-023-00673-4
• Shikhman, Vladimir. On local uniqueness of normalized Nash equilibria. In: Pure and Applied Functional Analysis, Vol. 8, no. 3., p. 1215-1228 (2023). http://yokohamapublishers.jp/online2/oppafa/vol8/p903.html
• Lämmel, Sebastian ; Shikhman, Vladimir. Cardinality-constrained optimization problems in general position and beyond. In: Pure and Applied Functional Analysis, Vol. 8, no. 4., p. 1107-1133 (2023). http://yokohamapublishers.jp/online2/oppafa/vol8/p1107.html

2022:

• Müller, David ; Shikhman, Vladimir. Network manipulation algorithm based on inexact alternating minimization. In: Computational Management Science, Vol. 19, p. 627-664 (2022). doi.org/10.1007/s10287-022-00429-9
• Lämmel, Sebastian ; Shikhman, Vladimir. On nondegenerate M-stationary points for sparsity constrained nonlinear optimization. In: Journal of Global Optimization, Vol. 82, p. 219-242 (2022). doi.org/10.1007/s10898-021-01070-7
• Müller, David ; Nesterov, Yurii ; Shikhman, Vladimir. Discrete choice prox-functions on the simplex. In: Mathematics of Operations Research, Vol. 47, p. 485-507 (2022). doi.org/10.1287/moor.2021.1136
• Shikhman, Vladimir. Topological approach to mathematical programs with switching constraints. In: Set-Valued and Variational Analysis, Vol. 30, p. 335-354 (2022). doi.org/10.1007/s11228-021-00581-5

2021:

• Müller, David ; Nesterov, Yurii ; Shikhman, Vladimir. Dynamic pricing under nested logit demand. In: Pure and Applied Functional Analysis, Vol. 6, no. 6, p. 1435-1451 (2021). http://yokohamapublishers.jp/online2/oppafa/vol6/p1435.html

2020:

• Lampariello, Lorenzo ; Sagratella, Simone ; Shikhman, Vladimir ; Stein, Oliver. Interactions between bilevel optimization and Nash games. In: "Bilevel Optimization: Advances and Next Challenges" (2020), Springer Optimization and Its Applications - 161, Springer, ISBN : 978-3-030-52118-9. doi.org/10.1007/978-3-030-52119-6

2018:

• Shikhman, Vladimir ; Nesterov, Yurii ; Ginsburgh, Victor. Power method tâtonnements for Cobb-Douglas economies. In: Journal of Mathematical Economics, Vol. 75, p. 84-92 (2018). doi.org/10.1016/j.jmateco.2017.12.010
• Nesterov, Yurii ; Shikhman, Vladimir. Dual subgradient method with averaging for optimal resource allocation. In: European Journal of Operational Research, Vol. 270, no. 3, p. 907-916 (2018).  doi.org/10.1016/j.ejor.2017.09.043
• Nesterov, Yurii ; Shikhman, Vladimir. Computation of Fisher-Gale equilibrium by auction. In: Journal of the Operations Research Society of China, Vol. 6, no. 3, p. 349-389 (2018). doi.org/10.1007/s40305-018-0195-5

2017:

• Nesterov, Yurii ; Shikhman, Vladimir. Distributed price adjustment based on convex analysis. In: Journal of Optimization Theory and Applications, Vol. 172, no. 2, p. 594-622 (2017). doi:10.1007/s10957-016-0975-1 

2016:

• Dorsch, Dominik ; Gomez, Walter ; Shikhman, Vladimir. Sufficient optimality conditions hold for almost all nonlinear semidefinite programs. In: Mathematical Programming, Vol. 158, no. 1, p. 77-97 (2016). doi:10.1007/s10107-015-0915-0
• Nesterov, Yurii ; Shikhman, Vladimir. Algorithmic principle of least revenue for finding market equilibria. In: "Optimization and Its Applications in Control and Data Science" (2016), Springer Optimization and Its Applications - 115, Springer, ISBN : 978-3-319-42054-7. doi:10.1007/978-3-319-42056-1_14
• Nesterov, Yurii ; Shikhman, Vladimir. Excessive revenue model of competitive markets. In: "Nonlinear Analysis and Optimization" (2016), Contemporary Mathematics - 659, AMS, ISBN : 978-1-4704-2904-1. dx.doi.org/10.1090/conm/659

2015:

• Nesterov, Yurii ; Shikhman, Vladimir. Quasi-monotone subgradient methods for nonsmooth convex minimization. In: Journal of Optimization Theory and Applications, Vol. 165, no. 3, p. 917-940 (2015). doi:10.1007/s10957-014-0677-5 

2014:

• Dorsch, Dominik ; Jongen, Hubertus Th. ; Ruckmann, Jan-J. ; Shikhman, Vladimir. On the local representation of piecewise smooth equations as a Lipschitz manifold. In: Journal of Mathematical Analysis and Applications, Vol. 411, no. 2, p. 916-930 (2014). doi:10.1016/j.jmaa.2013.10.029

2013:

• Dorsch, Dominik ; Jongen, Hubertus Th. ; Shikhman, Vladimir. Local models in equilibrium optimization. In: Pacific Journal of Optimization, Vol. 9, no. 2, p. 201-224 (2013). http://www.ybook.co.jp/online2/oppjo/vol9/p201.html
• Dorsch, Dominik ; Jongen, Hubertus Th. ; Shikhman, Vladimir. On structure and computation of generalized Nash equilibria. In: SIAM Journal on Optimization, Vol. 23, no. 1, p. 452-474 (2013). doi:10.1137/110822670
• Dorsch, Dominik ; Jongen, Hubertus Th. ; Shikhman, Vladimir. On intrinsic complexity of Nash equilibrium problems and bilevel optimization. In: Journal of Optimization Theory and Applications, Vol. 159, no. 3, p. 606-634 (2013). doi:10.1007/s10957-012-0210-7

2012:

• Jongen, Hubertus Th. ; Shikhman, Vladimir. Bilevel optimization: on the structure of the feasible set. In: Mathematical Programming, Vol. 136, no. 1, p. 65-89 (2012). doi:10.1007/s10107-012-0551-x
• Jongen, Hubertus Th. ; Shikhman, Vladimir ; Steffensen, Sonja. Characterization of strong stability for C-stationary points in MPCC. In: Mathematical Programming, Vol. 132, no. 1-2, p. 295-308 (2012). doi:10.1007/s10107-010-0396-0.
• Dorsch, Dominik ; Shikhman, Vladimir ; Stein, Oliver. Mathematical programs with vanishing constraints: critical point theory. In: Journal of Global Optimization, Vol. 52, no. 3, p. 591-605 (2012). doi:10.1007/s10898-011-9805-z
• Shikhman, Vladimir ; Stein, Oliver. On jet-convex functions and their tensor products. In: Optimization, Vol. 61, no. 6, p. 717-731 (2012). doi:10.1080/02331934.2011.619535

2011:

• Jongen, Hubertus Th. ; Shikhman, Vladimir. General semi-infinite programming: critical point theory. In: Optimization, Vol. 60, no. 7, p. 859-873 (2011). doi:10.1080/02331934.2010.543134
• Jongen, Hubertus Th. ; Shikhman, Vladimir. Generalized semi-infinite programming: the nonsmooth symmetric Reduction ansatz. In: SIAM Journal on Optimization, Vol. 21, no. 1, p. 193-211 (2011). doi:10.1137/100786757
• Dorsch, Dominik ; Jongen, Hubertus Th. ; Shikhman, Vladimir. On topological properties of min-max functions. In: Set-Valued and Variational Analysis, Vol. 19, no. 2, p. 237-253 (2011). doi:10.1007/s11228-010-0170-8

2010:

• Guerra Vazquez, Francisco ; Jongen, Hubertus Th. ; Shikhman, Vladimir. General semi-infinite programming: symmetric Mangasarian Fromovitz constraint qualification and the closure of the feasible set. In: SIAM Journal on Optimization, Vol. 20, no. 5, p. 2487-2503 (2010). doi:10.1137/090775294

2009:

• Guerra Vazquez, Francisco ; Jongen, Hubertus Th. ; Shikhman, Vladimir ; Ivanov Todorov, Maxim. Criteria for efficiency in vector optimization. In: Mathematical Methods of Operations Research, Vol. 70, no. 1, p. 35-46 (2009). doi:10.1007/s00186-008-0230-0
• Jongen, Hubertus Th. ; Shikhman, Vladimir ; Ruckmann, Jan-J.. MPCC: critical point theory. In: SIAM Journal on Optimization, Vol. 20, no. 1, p. 473-484 (2009). doi:10.1137/080733693
• Jongen, Hubertus Th. ; Shikhman, Vladimir ; Ruckmann, Jan-J.
  On Stability of the Feasible Set of a Mathematical Problem with Complementarity Problems
  
  
  Read More: https://epubs.siam.org/doi/abs/10.1137/08072694X
  On stability of the MPCC feasible set. In: SIAM Journal on Optimization, Vol. 20, no. 3, p. 1171-1184 (2009). doi:10.1137/08072694X

2008:

• Shikhman, Vladimir. A note on global optimization via heat diffusion eEquation. In: Journal of Global Optimization, Vol. 42, no. 4, p. 619-623 (2008). doi:10.1007/s10898-008-9281-2
• Shikhman, Vladimir ; Stein, Oliver. Constrained optimization: projected gradient flows. In: Journal of Optimization Theory and Applications, Vol. 139, no. 2, p. 117-130 (2008). doi:10.1007/s10957-008-9445-8