Methods of Nonsmooth Analysis as Applied to the Problem of Minimizing the Sum of Moduli of Affine Functions

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Methods of Nonsmooth Analysis as Applied to the Problem of Minimizing the Sum of Moduli of Affine Functions. / Tamasyan, G.S.; Shulga, G.S.

In: Journal of Applied and Industrial Mathematics, Vol. 18, No. 4, 2024, p. 875-885.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{2283e1cd463f4f7e916cc22793f7c96f,

title = "Methods of Nonsmooth Analysis as Applied to the Problem of Minimizing the Sum of Moduli of Affine Functions",

abstract = "Abstract: An application of constructive nonsmooth analysis methods to the problem of minimizinga convex piecewise affine function defined as the sum of absolute values of affine functions isdemonstrated. Hypodifferential calculus was used in the general (multidimensional) case, whilesubdifferential calculus was employed in the scalar case. Analyzing the optimality criterion, onecan reveal that the point delivering the global minimum can be found by solving thecorresponding linear programming problem. In the scalar case, the solution can also be found inclosed form as the weighted median of the nodes of a broken line. {\textcopyright} 2025 Elsevier B.V., All rights reserved.",

keywords = "broken line, hypodifferential, least absolute values, piecewise affine function, subdifferential, weighted median, Affine transforms, Global optimization, Absolute values, Affine function, Analysis method, Broken line, Hypodifferential, Least absolute value, Non-smooth analysis, Piecewise affine functions, Subdifferentials, Weighted median, Linear programming",

author = "G.S. Tamasyan and G.S. Shulga",

note = "Export Date: 01 November 2025; Cited By: 0; Correspondence Address: G.S. Tamasyan; Mozhaiskiy Space Military Academy, St. Petersburg, 197082, Russian Federation; email: grigoriytamasjan@mail.ru; G.S. Shulga; Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178, Russian Federation; email: gdextrous@gmail.com",

year = "2024",

doi = "10.1134/S1990478924040203",

language = "Английский",

volume = "18",

pages = "875--885",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "4",

}

RIS

TY - JOUR

T1 - Methods of Nonsmooth Analysis as Applied to the Problem of Minimizing the Sum of Moduli of Affine Functions

AU - Tamasyan, G.S.

AU - Shulga, G.S.

N1 - Export Date: 01 November 2025; Cited By: 0; Correspondence Address: G.S. Tamasyan; Mozhaiskiy Space Military Academy, St. Petersburg, 197082, Russian Federation; email: grigoriytamasjan@mail.ru; G.S. Shulga; Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178, Russian Federation; email: gdextrous@gmail.com

PY - 2024

Y1 - 2024

N2 - Abstract: An application of constructive nonsmooth analysis methods to the problem of minimizinga convex piecewise affine function defined as the sum of absolute values of affine functions isdemonstrated. Hypodifferential calculus was used in the general (multidimensional) case, whilesubdifferential calculus was employed in the scalar case. Analyzing the optimality criterion, onecan reveal that the point delivering the global minimum can be found by solving thecorresponding linear programming problem. In the scalar case, the solution can also be found inclosed form as the weighted median of the nodes of a broken line. © 2025 Elsevier B.V., All rights reserved.

AB - Abstract: An application of constructive nonsmooth analysis methods to the problem of minimizinga convex piecewise affine function defined as the sum of absolute values of affine functions isdemonstrated. Hypodifferential calculus was used in the general (multidimensional) case, whilesubdifferential calculus was employed in the scalar case. Analyzing the optimality criterion, onecan reveal that the point delivering the global minimum can be found by solving thecorresponding linear programming problem. In the scalar case, the solution can also be found inclosed form as the weighted median of the nodes of a broken line. © 2025 Elsevier B.V., All rights reserved.

KW - broken line

KW - hypodifferential

KW - least absolute values

KW - piecewise affine function

KW - subdifferential

KW - weighted median

KW - Affine transforms

KW - Global optimization

KW - Absolute values

KW - Affine function

KW - Analysis method

KW - Broken line

KW - Hypodifferential

KW - Least absolute value

KW - Non-smooth analysis

KW - Piecewise affine functions

KW - Subdifferentials

KW - Weighted median

KW - Linear programming

U2 - 10.1134/S1990478924040203

DO - 10.1134/S1990478924040203

M3 - статья

VL - 18

SP - 875

EP - 885

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 4

ER -

ID: 143409518