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. 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
2.
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
2019
3.
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
2017
4.
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, 3, 96–110; Autom. Remote Control, 78:3 (2017), 463–474
5.
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
6.
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
2016
7.
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
2015
8.
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, 1, 10–18
2014
9.
Yu. G. Evtushenko, M. A. Posypkin, “Method of non-uniform coverages to solve the multicriteria optimization problems with guaranteed accuracy”, Avtomat. i Telemekh., 2014, 6, 49–68; Autom. Remote Control, 75:6 (2014), 1025–1040
10.
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, 4, 3–11
11.
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
2013
12.
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
13.
Yu. G. Evtushenko, M. A. Posypkin, “Nonuniform covering method as applied to multicriteria optimization problems with guaranteed accuracy”, Zh. Vychisl. Mat. Mat. Fiz., 53:2 (2013), 209–224; Comput. Math. Math. Phys., 53:2 (2013), 144–157
2012
14.
M. A. Posypkin, A. V. Turkin, “An algorithm for regions extraction with corrupted ridge and valley structure”, Informatsionnye Tekhnologii i Vychslitel'nye Sistemy, 2012, 1, 52–59
15.
O. S. Zaikin, M. A. Posypkin, A. A. Semenov, “Using volunteer computation to solve cryptographic problems”, Prikl. Diskr. Mat. Suppl., 2012, 5, 107–108
2011
16.
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
2010
17.
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, 10, 156–166; Autom. Remote Control, 71:10 (2010), 2152–2161
18.
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
2008
19.
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
2007
20.
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
2006
21.
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
2005
22.
M. A. Posypkin, I. Kh. Sigal, “Investigation of algorithms for parallel computations in knapsack-type discrete optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 45:10 (2005), 1801–1809; Comput. Math. Math. Phys., 45:10 (2005), 1735–1742
2004
23.
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
1997
24.
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, 4, 58–59
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