1. Deterministic methods for mathematical programming problems.
2. Boolean knapsack problems.
3. Parallel and distributed computing methods in optimization.
Main publications:
Y. Evtushenko, M. Posypkin, “A deterministic approach to global box-constrained optimization”, Optimization Letters, 7:4 (2013), 819–829
Posypkin, Mikhail and Semenov, Alexander and Zaikin, Oleg, “Using BOINC desktop grid to solve large scale SAT problems”, Computer Science, 13:1 (2012), 25–34
Yu. G. Evtushenko, M. A. Posypkin., “Varianty metoda neravnomernykh pokrytii dlya globalnoi optimizatsii chastichno(tselochislennykh nelineinykh zadach.”, Doklady Akademii nauk, 437:2 (2011), 168–172
Kolpakov R.M., Posypkin M.A., “Verkhnyaya i nizhnyaya otsenki trudoemkosti metoda vetvei i granits dlya zadachi o rantse”, Diskretnaya matematika, 22:1 (2010), 58–73
Y. Evtushenko, M. Posypkin, I. Sigal, “A framework for parallel large-scale global optimization”, Computer Science – Research and Development, 23:3 (2009), 211–215
M. A. Posypkin, D. A. Sidnev, “Application of interval slopes in nonsmooth one-dimensional optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 65:3 (2025), 301–324; Comput. Math. Math. Phys., 65:3 (2025), 544–566
2023
2.
E. B. Barashov, A. V. Egorkin, D. V. Lemtyuzhnikova, M. A. Posypkin, “Efficiency of the reduction algorithms in the bin packing problem”, Sistemy i Sredstva Inform., 33:3 (2023), 61–75
M. V. Popov, M. A. Posypkin, “Approximation of the set of solutions of systems of nonlinear inequalities using graphic accelerators”, Inform. Primen., 14:3 (2020), 20–25
4.
G. A. Amirkhanova, A. Yu. Gorchakov, A. J. Duysenbaeva, M. A. Posypkin, “Multi-start method with deterministic restart mechanism”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 16:2 (2020), 100–111
R. M. Kolpakov, M. A. Posypkin, “Effective parallelization strategy for the solution of subset sum problems by the branch-and-bound method”, Diskr. Mat., 31:4 (2019), 20–37; Discrete Math. Appl., 30:5 (2020), 313–325
R. M. Kolpakov, M. A. Posypkin, Si Tu Tant Sin, “Complexity of solving the Subset Sum problem with the branch-and-bound method with domination and cardinality filtering”, Avtomat. i Telemekh., 2017, no. 3, 96–110; Autom. Remote Control, 78:3 (2017), 463–474
R. M. Kolpakov, M. A. Posypkin, “On the best choice of a branching variable in the subset sum problem”, Diskr. Mat., 29:1 (2017), 51–58; Discrete Math. Appl., 28:1 (2018), 29–34
Yu. G. Evtushenko, M. A. Posypkin, L. A. Rybak, A. V. Turkin, “Finding sets of solutions to systems of nonlinear inequalities”, Zh. Vychisl. Mat. Mat. Fiz., 57:8 (2017), 1248–1254; Comput. Math. Math. Phys., 57:8 (2017), 1241–1247
Yu. G. Evtushenko, S. A. Lurie, M. A. Posypkin, Yu. O. Solyaev, “Application of optimization methods for finding equilibrium states of two-dimensional crystals”, Zh. Vychisl. Mat. Mat. Fiz., 56:12 (2016), 2032–2041; Comput. Math. Math. Phys., 56:12 (2016), 2001–2010
Bo Tian, M. A. Posypkin, I. Kh. Sigal, “Load balancing in solving problems based on estimates of the computational complexity of subproblems”, Informatsionnye Tekhnologii i Vychslitel'nye Sistemy, 2015, no. 1, 10–18
2014
11.
Yu. G. Evtushenko, M. A. Posypkin, “Method of non-uniform coverages to solve the multicriteria optimization problems with guaranteed accuracy”, Avtomat. i Telemekh., 2014, no. 6, 49–68; Autom. Remote Control, 75:6 (2014), 1025–1040
M. O. Manzyuk, O. S. Zaikin, M. A. Posypkin, “CluBORun: tool for utilizing idle resources of computing clusters in BOINC computing”, Informatsionnye Tekhnologii i Vychslitel'nye Sistemy, 2014, no. 4, 3–11
13.
K. K. Abgaryan, M. A. Posypkin, “Optimization methods as applied to parametric identification of interatomic potentials”, Zh. Vychisl. Mat. Mat. Fiz., 54:12 (2014), 1994–2001; Comput. Math. Math. Phys., 54:12 (2014), 1929–1935
O. S. Zaikin, A. A. Semenov, M. A. Posypkin, “Constructing decomposition sets for distributed solution of sat problems in volunteer computing project sat@home”, UBS, 43 (2013), 138–156
M. A. Posypkin, A. V. Turkin, “An algorithm for regions extraction with corrupted ridge and valley structure”, Informatsionnye Tekhnologii i Vychslitel'nye Sistemy, 2012, no. 1, 52–59
17.
O. S. Zaikin, M. A. Posypkin, A. A. Semenov, “Using volunteer computation to solve cryptographic problems”, Prikl. Diskr. Mat. Suppl., 2012, no. 5, 107–108
2011
18.
Yu. G. Evtushenko, M. A. Posypkin, “An application of the nonuniform covering method to global optimization of mixed integer nonlinear problems”, Zh. Vychisl. Mat. Mat. Fiz., 51:8 (2011), 1376–1389; Comput. Math. Math. Phys., 51:8 (2011), 1286–1298
R. M. Kolpakov, M. A. Posypkin, I. Kh. Sigal, “On a lower bound on the computational complexity of a parallel implementation of the branch-and-bound method”, Avtomat. i Telemekh., 2010, no. 10, 156–166; Autom. Remote Control, 71:10 (2010), 2152–2161
R. M. Kolpakov, M. A. Posypkin, “Upper and lower bounds for the complexity of the branch and bound method for the knapsack problem”, Diskr. Mat., 22:1 (2010), 58–73; Discrete Math. Appl., 20:1 (2010), 95–112
R. M. Kolpakov, M. A. Posypkin, “Асимптотическая оценка сложности метода ветвей и границ с ветвлением по дробной переменной для задачи о ранце”, Diskretn. Anal. Issled. Oper., 15:1 (2008), 58–81
M. A. Posypkin, I. Kh. Sigal, “Application of parallel heuristic algorithms for speeding up parallel implementations of the branch-and-bound method”, Zh. Vychisl. Mat. Mat. Fiz., 47:9 (2007), 1524–1537; Comput. Math. Math. Phys., 47:9 (2007), 1464–1476
M. A. Posypkin, I. Kh. Sigal, “Speedup estimates for some variants of the parallel implementations of the branch-and-bound method”, Zh. Vychisl. Mat. Mat. Fiz., 46:12 (2006), 2289–2304; Comput. Math. Math. Phys., 46:12 (2006), 2187–2202
A. Ya. Kalinov, S. A. Klimov, M. A. Posypkin, G. I. Savin, S. D. Ustyugov, V. M. Chechëtkin, B. M. Shabanov, “Mathematical modeling of a supernova explosion on a parallel computer”, Zh. Vychisl. Mat. Mat. Fiz., 44:5 (2004), 953–960; Comput. Math. Math. Phys., 44:5 (2004), 903–910
M. A. Posypkin, “On closed classes containing precomplete classes of the set of all one-place functions”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1997, no. 4, 58–59