Linear programming and network flows (2nd ed.)
Linear programming and network flows (2nd ed.)
New branch-and-bound rules for linear bilevel programming
SIAM Journal on Scientific and Statistical Computing
Descent approaches for quadratic bilevel programming
Journal of Optimization Theory and Applications
Interval number and fuzzy number linear programmings
Fuzzy Sets and Systems
A Global Optimization Method for Solving Convex Quadratic Bilevel Programming Problems
Journal of Global Optimization
Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications)
Optimal value range in interval linear programming
Fuzzy Optimization and Decision Making
Journal of Global Optimization
| Hi-index | 7.29 |
In this paper, we address linear bilevel programs when the coefficients of both objective functions are interval numbers. The focus is on the optimal value range problem which consists of computing the best and worst optimal objective function values and determining the settings of the interval coefficients which provide these values. We prove by examples that, in general, there is no precise way of systematizing the specific values of the interval coefficients that can be used to compute the best and worst possible optimal solutions. Taking into account the properties of linear bilevel problems, we prove that these two optimal solutions occur at extreme points of the polyhedron defined by the common constraints. Moreover, we develop two algorithms based on ranking extreme points that allow us to compute them as well as determining settings of the interval coefficients which provide the optimal value range.