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Title: | A new method to solve bi-level quadratic linear fractional programming problems |
Authors: | Singh, Sanjeet P. Haldar, Nivedita |
Keywords: | Bi-level programming dual problem Linear fractional programming Quadratic linear fractional problem Quadratic programming Stackelberg game |
Issue Date: | 2015 |
Publisher: | SCOPUS International Game Theory Review World Scientific Publishing Co. Pte Ltd |
Series/Report no.: | 17(2) |
Abstract: | In this paper, we have developed a new method to solve bi-level quadratic linear fractional programming (BLQLFP) problems in which the upper-level objective function is quadratic and the lower-level objective function is linear fractional. In this method a BLQLFP problem is transformed into an equivalent single-level quadratic programming (QP) problem with linear constraints by forcing the duality gap of the lower-level problem to zero. Then by obtaining all vertices of the constraint region of the dual of the lower-level problem, which is a convex polyhedron, the single-level QP problem is converted into a series of finite number of QP problems with linear constraints which can be solved by any standard method for solving a QP. The best among the optimal solutions gives the desired optimal solution for the original bi-level programming (BLP) problem. Theoretical results have been illustrated with the help of a numerical example. � 2015 World Scientific Publishing Company. |
Description: | Singh, Sanjeet P., Operations Management Group, Indian Institute of Management Calcutta, DH Road, Joka, Kolkata, 700104, India; Haldar, Nivedita, Operations Management Group, Indian Institute of Management Calcutta, DH Road, Joka, Kolkata, 700104, India ISSN/ISBN - 02191989 DOI - 10.1142/S0219198915400174 |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-84928485390&doi=10.1142%2fS0219198915400174&partnerID=40&md5=d87408498518000c61bebbddb17f2595 https://ir.iimcal.ac.in:8443/jspui/handle/123456789/1335 |
Appears in Collections: | Operations Management |
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