相关论文: From Hopf-Lax formula to optimal weak transfer pla…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
We propose an energy-efficient procedure for transponder configuration in FMF-based elastic optical networks in which quality of service and physical constraints are guaranteed and joint optimization of transmit optical power, temporal,…
We consider two different variational models of transport networks, the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford-Shah image inpainting and techniques developed in that field,…
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…
We consider the problem of designing a stabilizing and optimal static controller with a pre-specified sparsity pattern. Since this problem is NP-hard in general, it is necessary to resort to approximation approaches. In this paper, we…
We consider the problem of estimating the states of weakly coupled linear systems from sampled measurements. We assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the…
In this paper, we introduce a generalized dynamical unbalanced optimal transport framework by incorporating limited control input and mass dissipation, addressing limitations in conventional optimal transport for control applications. We…
We construct a transport map from Poisson point processes onto ultra-log-concave measures over the natural numbers, and show that this map is a contraction. Our approach overcomes the known obstacles to transferring functional inequalities…
In this paper, we extend the scope of Caffarelli's contraction theorem, which provides a measure of the Lipschitz constant for optimal transport maps between log-concave probability densities in $\R^d$. Our focus is on a broader category of…
One of the most common control decisions faced by power system operators is the question of how to dispatch generation to meet demand for power. This is a complex optimization problem that includes many nonlinear, non convex constraints as…
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…
We study the safe reinforcement learning problem with nonlinear function approximation, where policy optimization is formulated as a constrained optimization problem with both the objective and the constraint being nonconvex functions. For…
By using optimal mass transport theory, we provide a direct proof to the sharp $L^p$-log-Sobolev inequality $(p\geq 1)$ involving a log-concave homogeneous weight on an open convex cone $E\subseteq \mathbb R^n$. The perk of this proof is…
We rephrase Monge's optimal transportation (OT) problem with quadratic cost--via a Monge-Amp\`ere equation--as an infinite-dimensional optimization problem, which is in fact a convex problem when the target is a log-concave measure with…
One revisits the standard saddle-point method based on conjugate duality for solving convex minimization problems. Our aim is to reduce or remove unnecessary topological restrictions on the constraint set. Dual equalities and…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…
We provide a Hop-Lax formula for variational problems with non-constant discount and deduce a dynamic programming equation. We also study some regularity properties of the value function.
We look into modeling fuel cell hybrid trains for the purpose of optimizing their operation using convex optimization. Models and constraints necessary to form a physically feasible yet convex problem are reviewed. This effort is described…
Flexible transmission line impedances on one hand are a promising control resource for facilitating grid flexibility, but on the other hand add much complexity to the concerned optimization problems. This paper develops a convexification…
We propose a two-stage algorithm for energy-efficient resource allocation constrained to QoS and physical requirements in OFDM-based EONs. The first stage deals with routing, grooming and traffic ordering and aims at minimizing amplifier…