non-smooth analysis, optimization, modeling of physical and economic processes, difference of convex functions
Biography
postgraduate and doctoral studies at St. Petersburg University
Main publications:
Proudnikov I., “New constructions for local approximation of Lipschitz functions.”, Nonlinear Analysis, 54:3 (2003), 373-390
Proudnikov I., “New constructions for local approximation of Lipschitz functions. II”, Nonlinear Analysis, 66:7 (2007), 1443-1453
Прудников И., “On the question of the representability of a function of two variables as a difference of convex functions.”, Siberian Mathematical Journal RAS, 55:6 (2014), 1368-1380.
Proudnikov I., “Subdifferentials of the First and Second Orders for Lipschitz Functions”, J. of Optimization Theory and Application, 171:3 (2016), 906-930
Proudnikov I., “On continuous codifferentiability of
quasidifferentiable functions
SN”, s43069-021-00085-w, Oper. Res. Forum 2, 44 (2021)., 44 (2021)
I. M. Prudnikov, “On the representability of a function of two variables as the difference of two convex functions”, Sibirsk. Mat. Zh., 55:6 (2014), 1368–1380; Siberian Math. J., 55:6 (2014), 1116–1125
I. M. Proudnikov, “A method of construction of exhaustive family of upper convex approximations”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2013, no. 1, 37–51
2010
3.
I. M. Prudnikov, “$C^2(D)$-integral approximation of nonsmooth functions conserving $\varepsilon(D)$-extremum points”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:5 (2010), 159–169
2009
4.
I. M. Prudnikov, “The average value of profit in infinite coalition games”, Mat. Teor. Igr Pril., 1:4 (2009), 111–124
2003
5.
I. M. Prudnikov, “Procedures for the lower convex approximations construction”, Zh. Vychisl. Mat. Mat. Fiz., 43:7 (2003), 939–950; Comput. Math. Math. Phys., 43:7 (2003), 896–907
I. M. Prudnikov, “The Use of Certain Equations of Mathematical Physics in Optimization of a Function on a Set. II”, Avtomat. i Telemekh., 2002, no. 12, 32–40; Autom. Remote Control, 63:12 (2002), 1891–1899
7.
I. M. Prudnikov, “The Use of Certain Equations of Mathematical Physics in Optimization of a Function on a Set. I”, Avtomat. i Telemekh., 2002, no. 11, 76–87; Autom. Remote Control, 63:11 (2002), 1764–1774
2000
8.
I. M. Prudnikov, “Lower convex approximations of Lipschitzian functions”, Zh. Vychisl. Mat. Mat. Fiz., 40:3 (2000), 378–386; Comput. Math. Math. Phys., 40:3 (2000), 359–367
I. M. Prudnikov, “Application of the Method of Potentials to the Function Optimization over the Set Specified by Linear Inequalities”, Avtomat. i Telemekh., 1996, no. 1, 66–82; Autom. Remote Control, 57:1 (1996), 53–66
1994
11.
I. M. Prudnikov, “Differential properties of the extremum function with respect to a Lipschitzian many-valued mapping”, Zh. Vychisl. Mat. Mat. Fiz., 34:10 (1994), 1347–1357; Comput. Math. Math. Phys., 34:10 (1994), 1169–1177
I. M. Prudnikov, “A method for the global optimization of a function and an estimate for the rate of its convergence”, Avtomat. i Telemekh., 1993, no. 12, 72–81; Autom. Remote Control, 54:12 (1993), 1785–1793
I. M. Prudnikov, “Necessary and sufficient conditions for the representability of a positive homogeneous function of three variables in the form of a difference of convex functions”, Izv. RAN. Ser. Mat., 56:5 (1992), 1116–1128; Russian Acad. Sci. Izv. Math., 41:2 (1993), 377–387
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