Lexicographic regularization and duality for improper linear programming problems

A new approach to the optimal lexicographic correction of improper linear programming problems is proposed. The approach is based on the multistep regularization of the classical Lagrange function with respect to primal and dual variables simultaneously. The regularized function can be used as a bas...

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Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics Vol. 295; no. Suppl 1; pp. 131 - 144
Main Authors: Popov, L. D., Skarin, V. D.
Format: Journal Article Conference Proceeding
Language:English
Published: Moscow Pleiades Publishing 01.12.2016
Springer Nature B.V
Subjects:
Linear programming
Mathematics
Mathematics and Statistics
Numerical stability
Regularization
generalized solutions
linear programming
improper problems
penalty methods
duality
regularization
ISSN:0081-5438, 1531-8605
Online Access:Get full text
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Summary:A new approach to the optimal lexicographic correction of improper linear programming problems is proposed. The approach is based on the multistep regularization of the classical Lagrange function with respect to primal and dual variables simultaneously. The regularized function can be used as a basis for generating new duality schemes for problems of this kind. Theorems on the convergence and numerical stability of the method are presented, and an informal interpretation of the obtained generalized solution is given.
Bibliography:ObjectType-Article-1
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SourceType-Conference Papers & Proceedings-1
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ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543816090145