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In this paper, the bilevel programming model for CNDPs is transferred into a single level optimization problem by virtue of a marginal function tool.
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.
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.
By exploring the inherent nature of the CNDP, the marginal function for the lower-level user equilibrium problem is proved to be continuously differentiable and its functional value and derivative in link capacity enhancement can be obtained efficiently by implementing a user equilibrium assignment subroutine.
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.
Then, the marginal function V defined on X by. is upper semi-continuous at x0. Lemma 2.3.
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Regarding cases with cyclic graphs, the iterative process described above must follow a message-passing schedule to compute approximations of the true marginal functions.
The results related to the convergence of marginal functions and approximated solutions were given and the case of data perturbations was also considered.
Considering the significant alleviating influence of seeking support from any resource on PTSD symptoms, these observations indicated the existence of various mental health support resources in Afghanistan society, and their marginal functioning in coping with severe traumatic experiences.
A practical framework for generating cross correlated random fields with a specified marginal distribution function, an autocorrelation function and cross correlation coefficients is presented in the paper.
Considering a prospect-theory type marginal utility function, the S-shape value function is utilized to encode the preferences of negotiators.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com