# American Institute of Mathematical Sciences

March  2019, 9(1): 45-52. doi: 10.3934/naco.2019004

## 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

Received  November 2017 Revised  May 2018 Published  October 2018

Fund Project: 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).

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.

Citation: Rui Qian, Rong Hu, Ya-Ping Fang. Local smooth representation of solution sets in parametric linear fractional programming problems. Numerical Algebra, Control & Optimization, 2019, 9 (1) : 45-52. doi: 10.3934/naco.2019004
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