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Algorithmic insights and a convergence analysis for a Karmarkar‐type of algorithm for linear programming problems
Author(s) -
Sherali Hanif D.
Publication year - 1987
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198706)34:3<399::aid-nav3220340307>3.0.co;2-6
Subject(s) - subgradient method , convergence (economics) , linear programming , algorithm , mathematical optimization , mathematics , lagrange multiplier , type (biology) , computer science , ecology , economics , biology , economic growth
This paper is concerned with a modification of a recently proposed variant of Karmarkar's algorithm for solving linear programming problems. In analyzing this variant, we exhibit interesting and useful relationships of these types of algorithms with barrier function methods, and subgradient optimization procedures involving space dilation techniques, which subsume the well‐known ellipsoidal type of algorithms. Convergence of this variant is established under certain regularity conditions. We also provide remarks on how to obtain dual variables or Lagrange multipliers at optimality.