О задаче минимизации суммы модулей аффинных функций

Translated title of the contribution: ON THE PROBLEM OF MINIMIZING THE SUM OF MODULES OF AFFINE FUNCTIONS

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Abstract

In the present paper one nonsmooth problem to unconditional extremum is considered. It is required to find a minimum of the sum of modules of affine functions. Such a problem occurs in a number of applied engineering, economic and mathematical tasks. This problem is traditionally belongs to the class of piecewise linear programming. Approach based on reducing the problem under investigation to a linear programming problem is most widely used. The development of more efficient computational algorithms continues from the middle 60s to the present day. The paper proposes a new method that using apparatus of constructive nonsmooth analysis. Namely, by applying the hypodifferential calculus, an optimality criterion is obtained. Verification of this criterion is reduced to the sequential solution of two linear programming problems of smaller dimension, that has a positive effect to reducing the complexity of finding a solution to the original problem.
Translated title of the contributionON THE PROBLEM OF MINIMIZING THE SUM OF MODULES OF AFFINE FUNCTIONS
Original languageRussian
Pages (from-to)471-475
Number of pages5
JournalПроцессы управления и устойчивость
Volume6
Issue number1
StatePublished - 2019

Keywords

  • METHOD OF LEAST MODULES
  • linear programming
  • PIECEWISE LINEAR PROGRAMMING
  • AFFINE FUNCTIONS
  • SYSTEM OF LINEAR INEQUALITIES
  • HYPODIFFERENTIAL
  • nonsmooth analysis

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