The strict complementary slackness condition in linear fractional programming

TL;DR

This paper extends the strict complementary slackness condition from linear programming to linear fractional programming, demonstrating the existence of such solutions and providing methods to find them.

Contribution

It introduces the SCSC concept into LFP, proves the existence of strict complementary solutions, and develops procedures to identify these solutions using LP techniques.

Findings

Existence of strict complementary solutions in LFP

Reduction of the problem to finding a relative interior point

Development of two procedures for solution identification

Abstract

The strict complementary slackness condition (SCSC) is an important concept in the duality theory of linear programming (LP). The current study aims at extending this concept to the framework of linear fractional programming (LFP). First, we define this concept in this framework and demonstrate the existence of a strict complementary solution - a pair of primal and dual optimal solutions satisfying the SCSC. Second, we show that the problem of finding such a solution reduces to that of identifying a relative interior point of a polyhedron. More recently, Mehdiloozad et al. (2016) have addressed the latter problem by proposing an LP problem. Using their proposed LP problem, we finally develop two procedures for finding a strict complementary solution.