相关论文: From Hopf-Lax formula to optimal weak transfer pla…

Weak optimal transport generalizes the classical theory of optimal transportation to nonlinear cost functions and covers a range of problems that lie beyond the traditional theory - including entropic transport, martingale transport, and…

In this paper, we investigate stochastic versions of the Hopf-Lax formula which are based on compositions of the Hopf-Lax operator with the transition kernel of a L\'evy process taking values in a separable Banach space. We show that,…

We investigate the optimal mass transport problem associated to the following "ballistic" cost functional on phase space $M\times M^*$, $$ b_T(v, x):=\inf\{\langle v, \gamma (0)\rangle +\int_0^TL(\gamma (t), {\dot \gamma}(t))\, dt, \gamma…

In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\ell_0$ pseudo norm…

Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the…

The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…

We consider a model-independent pricing problem in a fixed-income market and show that it leads to a weak optimal transport problem as introduced by Gozlan et al. We use this to characterize the extremal models for the pricing of caplets on…

We consider the problem of obtaining interpolation constraints for function classes, i.e., necessary and sufficient constraints that a set of points, function values and (sub)gradients must satisfy to ensure the existence of a global…

An optimal transport problem on finite spaces is a linear program. Recently, a relaxation of the optimal transport problem via strictly convex functions, especially via the Kullback--Leibler divergence, sheds new light on data sciences.…

We introduce a new variant of the weak optimal transport problem where mass is distributed from one space to the other through unnormalized kernels. We give sufficient conditions for primal attainment and prove a dual formula for this…

We develop connections between Harnack inequalities for the heat flow of diffusion operators with curvature bounded from below and optimal transportation. Through heat kernel inequalities, a new isoperimetric-type Harnack inequality is…

In order to circumvent the difficulties in solving numerically the discrete optimal transport problem, in which one minimizes the linear target function $P\mapsto\langle C,P\rangle:=\sum_{i,j}C_{ij}P_{ij}$, Cuturi introduced a variant of…

This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…

We show that a certain entropy-like function is convex, under an optimal transport problem that is adapted to Ricci flow. We use this to reprove the monotonicity of Perelman's reduced volume.

This paper investigates the offline packet-delay-minimization problem for an energy harvesting transmitter. To overcome the non-convexity of the problem, we propose a C2-diffeomorphic transformation and provide the necessary and sufficient…

This is our first paper on the extension of our recent work on the Lax-Oleinik commutators and its applications to the intrinsic approach of propagation of singularities of the viscosity solutions of Hamilton-Jacobi equations. We…

We consider the problem of optimal path planning on a manifold which is the image of a smooth function. Optimal path-planning is of crucial importance for motion planning, image processing, and statistical data analysis. In this work, we…

We study an optimal weak transport cost related to the notion of convex order between probability measures. On the real line, we show that this weak transport cost is reached for a coupling that does not depend on the underlying cost…

We consider the problem of controlling a vehicle to arrive at a fixed destination while minimizing a combination of energy consumption and travel time. Our model includes vehicle speed and accelaration limits, aerodynamic drag, rolling…

In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of…