Local smooth representation of solution sets in parametric linear fractional programming problems

Rui Qian; Rong Hu; Ya-Ping Fang

doi:10.3934/naco.2019004

Article Contents

2019, Volume 9, Issue 1: 45-52. Doi: 10.3934/naco.2019004

This issue Previous Article Stability preservation in Galerkin-type projection-based model order reduction Next Article On construction of upper and lower bounds for the HOMO-LUMO spectral gap

Local smooth representation of solution sets in parametric linear fractional programming problems

1.
Department of Mathematics, Sichuan University, Chengdu 610065, P. R. China
2.
Department of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, P. R. China
3.
Department of Mathematics, Sichuan University, Chengdu 610065, P. R. China

* Corresponding author: Y. P. Fang
* Corresponding author: Y. P. Fang

Received: November 2017

Revised: May 2018

Published: March 2019

This work was partially supported by the National Science Foundation of China (No. 11471230)and the Scientific Research Foundation of the Education Department of Sichuan Province (No.16ZA0213)

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Abstract

The purpose of this paper is to investigate the structure of the solution sets in parametric linear fractional programming problems. It is shown that the solution set of a parametric linear fractional programming problem with smooth data has a local smooth representation. As a consequence, the corresponding marginal function is differentiable and the solution map admits a differentiable selection. We also give an example to illustrate the result.

Keywords:

Parametric linear fractional programming problem,
solution set,
sensitivity analysis,
smooth representation,
polyhedral convex set.

Mathematics Subject Classification: Primary: 90C31, 90C32.

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