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In this paper, we study a spline collocation method for a numerical solution to the optimal transport problem We mainly solve the \MAE with the second boundary condition numerically by proposing a center matching algorithm. We prove a…
In fuzzy decision-making processes based on linguistic information, operations on discrete fuzzy numbers are commonly performed. Aggregation and defuzzification operations are some of these often used operations. Many aggregation and…
Numerical methods for the optimal transport problem is an active area of research. Recent work of Kitagawa and Abedin shows that the solution of a time-dependent equation converges exponentially fast as time goes to infinity to the solution…
In this work we present a numerical method for the Optimal Mass Transportation problem. Optimal Mass Transportation (OT) is an active research field in mathematics.It has recently led to significant theoretical results as well as…
In this paper we present a novel method for the numerical solution of linear transport equations, which is based on ridgelets. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that…
We investigate the transportation problem under a Monge cost structure and derive compact formulas for optimal dual solutions based on the northwest-corner rule. As an application illustrating how these formulas yield structural insight…
In this paper, the optimal deployment of multiple unmanned aerial vehicles (UAVs) acting as flying base stations is investigated. Considering the downlink scenario, the goal is to minimize the total required transmit power of UAVs while…
The travelling thief problem (TTP) is a well-known multi-component optimisation problem that captures the interdependence between two components: the tour across cities and the packing of items. The packing while travelling problem (PWT) is…
We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…
We consider the following variant of the Monge-Kantorovich transportation problem. Let S be a finite set of point sites in d dimensions. A bounded set C in d-dimensional space is to be distributed among the sites p in S such that (i) each p…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
We re-examine a practical aspect of combinatorial fuzzy problems of various types, including search, counting, optimization, and decision problems. We are focused only on those fuzzy problems that take series of fuzzy input objects and…
In machine learning, Optimal Transport (OT) theory is extensively utilized to compare probability distributions across various applications, such as graph data represented by node distributions and image data represented by pixel…
It is well known over the recent years that measuring the success of projects under the umbrella of project management is inextricably linked with the associated cost, time, and quality. Most of the previous researches in the field assigned…
Optimal transport has recently started to be successfully employed to define misfit or loss functions in inverse problems. However, it is a problem intrinsically defined for positive (probability) measures and therefore strategies are…
We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…
We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference. More specifically, we develop a theory of…
We investigate the optimal transport problem between probability measures when the underlying cost function is understood to satisfy a least action principle, also known as a Lagrangian cost. These generalizations are useful when connecting…
The optimal transportation problem, first suggested by Gaspard Monge in the 18th century and later revived in the 1940s by Leonid Kantorovich, deals with the question of transporting a certain measure to another, using transport maps or…
In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between…