In this paper, the bilevel programming model for CNDPs is transferred into a single level optimization problem by virtue of a marginal function tool.
Given a real function u ( x ) on X, we define a value function (called also a marginal function) of u by β ( x ) = inf z ∈ T ( x ) u ( z ).
In addition, it leads to speculation that toxb might at one time have had a marginal function in pathogenesis, but that the lack of TEs in the SD20-NP genome, and therefore, the lack of opportunity to expand, resulted in pseudogenization.
The psychological stress induced during the debris reverse logistic process is the integral of an increasing marginal function of the waiting time for medical treatment and debris removal.
In applications of convex analysis it is important to be able to calculate the subdifferentials of various combinations of (proper and lower semicontinuous) convex functions, such as the sum of two such functions, or their inf-convolution ("epi-sum"), as well as the pre-composition of a convex function with an affine map or the "marginal" function obtained from a convex function and a linear map.
Following an exploration of the properties of the lower-level traffic equilibrium sub-problem, the bi-level optimal toll design problem is solved by a recently developed efficient marginal function approach.
In order to analyze the bilevel value function φ p o ( x, y ) and φ p p o ( x ), we consider a general 'abstract' framework of the marginal function: μ ( x ) = min y { ψ ( x, y ) ∣ y ∈ Ξ ( x ) }, (3.14).
On the other hand, by stability we mean the qualitative analysis, that is, the study of various continuity properties of the perturbation (or marginal) function (or map) of a family of parametrized vector optimization problems.
Usually, by stability, we mean the qualitative analysis, which is the study of various continuity properties of the perturbation or marginal function or map of a family of parametrized optimization problems.
The functional liver remnant after RE is hard to predict, due to the heterogeneity of the radiation-absorbed dose distribution, but may be crucial to prevent (severe) radioembolization-induced liver disease (REILD), especially in patients with a marginal liver function, as seen in cirrhosis or after chemotherapy.
For the significant coefficients we transformed these coefficients of the logit regression into percentages using a marginal effect function in Stata (mfx, predict (p) – see Results section).
