An application of an interior point method for problems with uncertainty

Altman, A. (1994). An application of an interior point method for problems with uncertainty. In: Operations Research ’93. pp. 5-7 Germany: Physica-Verlag HD. ISBN 978-3-642-46955-8 10.1007/978-3-642-46955-8_2.

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Abstract

Interior point methods (IPM) were first proposed for linear programming (LP) problems. Since 1984, when Karmarkar published his famous paper (Karmarkar (1984)), IPM were rapidly developed and improved. It is now widely accepted that the primal-dual logarithmic barrier method is the most efficient IPM. The idea of IPM was not restricted to linear programming alone. These methods quickly spread to quadratic, nonlinear and integer programming. The developments in quadratic programming (QP) are closely parallel to those in LP. While theoretical worst-case behaviour for LP and QP are the same, QP problems are harder to solve in practice. The derivation of the higher order primal-dual method for QP is analogous to the derivation for the linear case presented in Mehrotra (1991) and implemented by Altman and Gondzio (1992).

Item Type:	Book Section
Additional Information:	(1) Extended Abstracts of the 18th Symposium on Operations Research held at the University of Cologne September 1–3, 1993. (2) This work was done during the author’s stay at the International Institute for Applied Systems Analysis, Laxenburg, Austria
Research Programs:	Optimization under Uncertainty (OPT)
Depositing User:	Romeo Molina
Date Deposited:	04 May 2016 11:33
Last Modified:	27 Aug 2021 17:41
URI:	https://pure.iiasa.ac.at/13110

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