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We present an optimization-based approach to stochastic control problems with nonclassical information structures. We cast these problems equivalently as optimization prob- lems on joint distributions. The resulting problems are necessarily…
The offset optimization problem seeks to coordinate and synchronize the timing of traffic signals throughout a network in order to enhance traffic flow and reduce stops and delays. Recently, offset optimization was formulated into a…
We address the problem of identifying the dynamical law governing the evolution of a population of indistinguishable particles, when only aggregate distributions at successive times are observed. Assuming a Markovian evolution on a discrete…
We consider the speed planning problem for a vehicle moving along an assigned trajectory, under maximum speed, tangential and lateral acceleration, and jerk constraints. The problem is a nonconvex one, where nonconvexity is due to jerk…
In this work, we solve a discrete optimal transport problem in a nonuniform environment. To solve the optimal transport problem, we build the cost matrix and then use classical solvers for discrete optimal transport. The challenge is to…
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 reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous…
The problem of optimization on Stiefel manifold, i.e., minimizing functions of (not necessarily square) matrices that satisfy orthogonality constraints, has been extensively studied. Yet, a new approach is proposed based on, for the first…
Pose Graph Optimization involves the estimation of a set of poses from pairwise measurements and provides a formalization for many problems arising in mobile robotics and geometric computer vision. In this paper, we consider the case in…
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…
The optimal power flow (OPF) problem minimizes power system operating cost subject to both engineering and network constraints. With the potential to find global solutions, significant research interest has focused on convex relaxations of…
We propose an optimization approach to design cost-effective electrical power transmission networks. That is, we aim to select both the network structure and the line conductances (line sizes) so as to optimize the trade-off between network…
In the freeway network control (FNC) problem, the operation of a traffic network is optimized using only flow control. For special cases of the FNC problem, in particular the case when all merging flows are controlled, there exist tight…
This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…
We consider optimization methods for convex minimization problems under inexact information on the objective function. We introduce inexact model of the objective, which as a particular cases includes $(\delta,L)$ inexact oracle and…
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…
We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by…
In this paper we address the speed planning problem for a vehicle along a predefined path. A weighted average of two (conflicting) terms, energy consumption and travel time, is minimized. After deriving a non-convex mathematical model of…