On ϵ-solutions for robust fractional optimization problems

Jae Hyoung Lee,Gue Myung Lee

doi:10.1186/1029-242x-2014-501

Jae Hyoung Lee, Gue Myung Lee

Open Access

https://doi.org/10.1186/1029-242x-2014-501

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Abstract

We consider ϵ-solutions (approximate solutions) for a fractional optimization problem in the face of data uncertainty. Using robust optimization approach (worst-case approach), we establish optimality theorems and duality theorems for ϵ-solutions for the fractional optimization problem. Moreover, we give an example illustrating our duality theorems. MSC:90C25, 90C32, 90C46.

Highlights

1 Introduction A robust fractional optimization problem is to optimize an objective fractional function over the constrained set defined by functions with data uncertainty
We show that u∈U epi(f (·, u))∗ is closed
}. we formulate a dual problem (RFD) for (RFP) as follows: (RFD) max r s.t

Summary

Introduction

A robust fractional optimization problem is to optimize an objective fractional function over the constrained set defined by functions with data uncertainty.To get the -solution (approximate solution), many authors have established -optimality conditions and -duality theorems for several kinds of optimization problems [ – ]. They [ ] established optimality theorems and duality theorems for -solutions for convex optimization problems with uncertainty data. [ , ] Let hi : Rn → R ∪ {+∞}, i ∈ I (where I is an arbitrary index set), be a proper lower semicontinuous convex function.

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