Open AccessPessimistic Bilevel Linear Optimization
Author(s) -
Stephan Dempe,
Luo Guimei,
Susanne Franke
Publication year - 2018
Publication title -
journal of nepal mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2616-0161
pISSN - 2616-0153
DOI - 10.3126/jnms.v1i1.42165
Subject(s) - bilevel optimization , duality (order theory) , mathematical optimization , pessimism , transformation (genetics) , optimization problem , strong duality , mathematics , linear programming , global optimization , computer science , discrete mathematics , philosophy , biochemistry , chemistry , epistemology , gene
In this paper, we investigate the pessimistic bilevel linear optimization problem (PBLOP). Based on the lower level optimal value function and duality, the PBLOP can be transformed to a single-level while nonconvex and nonsmooth optimization problem. By use of linear optimization duality, we obtain a tractable and equivalent transformation and propose algorithms for computing global or local optimal solutions. One small example is presented to illustrate the feasibility of the method.