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Full-Text Articles in Social and Behavioral Sciences
On Asymptotic Behaviour And W 2, P Regularity Of Potentials In Optimal Transportation, Jiakun Liu, Neil Trudinger, Xu-Jia Wang
On Asymptotic Behaviour And W 2, P Regularity Of Potentials In Optimal Transportation, Jiakun Liu, Neil Trudinger, Xu-Jia Wang
Faculty of Engineering and Information Sciences - Papers: Part A
© 2014, Springer-Verlag Berlin Heidelberg. In this paper we study local properties of cost and potential functions in optimal transportation. We prove that in a proper normalization process, the cost function is uniformly smooth and converges locally smoothly to a quadratic cost x · y, while the potential function converges to a quadratic function. As applications we obtain the interior W2, p estimates and sharp C1, α estimates for the potentials, which satisfy a Monge–Ampère type equation. The W2, p estimate was previously proved by Caffarelli for the quadratic transport cost and the associated standard Monge–Ampère equation.
Global Optimization Method For Robust Pricing Of Transportation Networks Under Uncertain Demand, Shuaian Wang, Lauren Gardner, S.Travis Waller
Global Optimization Method For Robust Pricing Of Transportation Networks Under Uncertain Demand, Shuaian Wang, Lauren Gardner, S.Travis Waller
Faculty of Engineering and Information Sciences - Papers: Part A
We extend the existing toll pricing studies with fixed demand to stochastic demand. A new and practical second-best pricing problem with uncertain demand is proposed and formulated as a stochastic mathematical program with equilibrium constraints. In view of the problem structure, we develop a tailored global optimization algorithm. This algorithm incorporates a sample average approximation scheme, a relaxation-strengthening method, and a linearization approach. The proposed global optimization algorithm is applied to three networks: a two-link network, a seven-eleven network and the Sioux-Falls network. The results demonstrate that using a single fixed estimation of future demand may overestimate the future system …
Optimal Transportation On The Hemisphere, Sun-Yung Alice Chang, Jiakun Liu, Paul Yang
Optimal Transportation On The Hemisphere, Sun-Yung Alice Chang, Jiakun Liu, Paul Yang
Faculty of Engineering and Information Sciences - Papers: Part A
In this paper, we study the optimal transportation on the hemisphere, with the cost function c(x, y) = 1/2d2 (x, y), where d is the Riemannian distance of the round sphere. The potential function satisfies a Monge-Ampere type equation with natural boundary condtion. In this critical case, the hemisphere does not satisfy the c-convexity assumption. We obtain the priori oblique derivate estimate, and in the special case of two demensional hemisphere, we obtain the boundary C2 estimate. Our proof does not require the smoothness of densities.
Efficiency And Equity Of Speed Limits In Transportation Networks, Shuaian Wang
Efficiency And Equity Of Speed Limits In Transportation Networks, Shuaian Wang
Faculty of Engineering and Information Sciences - Papers: Part A
This paper examines the impact of speed limits on network efficiency, in terms of total travel time of all road users, and equity among road users from different origin-destination (OD) pairs, in terms of the change of travel time after imposing a speed limit scheme. We find that after imposing a speed limit scheme, the total travel time of all road users may decrease or increase; road users of some OD pairs may experience longer travel time, while other OD pairs may have shorter travel time. In view of the importance of speed limits on network efficiency and equity, we …
Regularity Of Monge-Ampere Equations In Optimal Transportation, Jiakun Liu
Regularity Of Monge-Ampere Equations In Optimal Transportation, Jiakun Liu
Faculty of Engineering and Information Sciences - Papers: Part A
We consider some recent regularity results for the Monge-Ampère equation arising in the optimal transportation problem. The Monge-Ampère equation under consideration has the following type
Regularity In Optimal Transportation, Jiakun Liu, Neil Trudinger, Xu-Jia Wang
Regularity In Optimal Transportation, Jiakun Liu, Neil Trudinger, Xu-Jia Wang
Faculty of Engineering and Information Sciences - Papers: Part A
In this talk, we give some estimates for solutions to the Monge-Amp`ere equation arising in optimal transportation. The Monge-Amp`ere equation under consideration has the following type