Sentence examples for by a bilevel programming from inspiring English sources
The continuous network design problem (CNDP) is characterized by a bilevel programming model and recognized to be one of the most difficult and challenging problems in transportation.
When there is uncertainty in the lower level optimization problem of a bilevel programming, it can be formulated by a robust optimization method as a bilevel programming problem with lower level second-order cone program (SOCBLP).
When there is uncertainty in the lower level optimization problem of a bilevel programming [1], it can be formulated by a robust optimization method as a bilevel programming problem having second-order cone programming [2] as its lower level problem, i.e., a bilevel programming problem with lower level second-order cone programs (SOCBLP).
When multiple followers are involved in a bilevel programming problem, the leader's decision will be affected by the reactions of these followers.
In this paper, we consider a bilevel programming problem (BP), which is called semivectorial bilevel programming problem by Bonnel and Morgan [1], where the upper level is a scalar optimization problem and the lower level is a vector optimization problem: (BP): ' min x ' F ( x, z ) (1.1).
The interaction of these agents is modeled as a bilevel programming problem.
A bilevel programming technique can be used to formulate this equilibrium network design problem.
Clearly, the above problem is a bilevel programming problem with interval coefficients in both objective functions only.
TNDP is formulated as a bilevel programming problem, which is difficult to solve on account of its combinatorial nature.
The result obtained is then used to develop a necessary and sufficient local optimality condition for a bilevel programming with SOC as its lower level problem.
The rule established is then applied to deriving a necessary and sufficient local optimality condition for a bilevel programming with a second-order cone constrained lower level problem.
