最优化与控制
Coordinated truck-and-drone routing integrates the high capacity and range of ground vehicles with the flexible routing and speed of drones, enabling simultaneous service. Increasingly applied in last-mile delivery, this synchronization…
A generalized Nash equilibrium problem (GNEP) in Banach space consists of $N>1$ optimal control problems with couplings in both the objective functions and, most importantly, in the feasible sets. We address the existence of equilibria for…
Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…
Tipping points characterize situations where a regulated system may experience a sudden and irreversible change and are generally associated with a random state of the system below which the change materializes. In this paper, we study a…
We establish a systematic solution method for optimal stopping problems of spectrally negative L\'evy processes. Our approach relies essentially on the potential theory, in particular the Riesz decomposition and the maximum principle. Using…
In this paper, we study the use of outer metrics, in particular Sobolev-type metrics on the diffeomorphism group in the context of PDE-constrained shape optimization. Leveraging the structure of the diffeomorphism group we analyze the…
We introduce a novel framework for decentralized projection-free optimization, extending projection-free methods to a broader class of upper-linearizable functions. Our approach leverages decentralized optimization techniques with the…
This paper deals with the gradient stability and the gradient stabilizability of Caputo time fractional diffusion linear systems. First, we give sufficient conditions that allow the gradient Mittag-Leffler and strong stability, where we use…
The quadratically regularized optimal transport problem is empirically known to have sparse solutions: its optimal coupling $\pi_{\varepsilon}$ has sparse support for small regularization parameter $\varepsilon$, in contrast to entropic…
This paper presents an online learning-based adaptive control framework for density-matrix tracking in a two-level Lindblad-Gorini-Kossakowski-Sudarshan (LGKS) quantum system, in which the feedback control law does not require prior…
This paper investigates the asymptotic behavior of the solution to a linear-quadratic stochastic optimal control problems. The so-called probability cell problem is introduced the first time. It serves as the probability interpretation of…
We investigate optimization models for the purpose of computational redistricting. Our focus is on nonconvex objectives for estimating expected Black Representatives and Political Representation. The objectives are a composition of a ratio…
We provide an explicit algorithm to solve the idempotent analogue of the discrete Monge-Kantorovich optimal mass transportation problem with the usual real number field replaced by the tropical (max-plus) semiring, in which addition is…
We study a class of stochastic optimal design problems for elliptic partial differential equations in divergence form, where the coefficients represent mixtures of two conducting materials. The objective is to minimize a generalized risk…
This work studies how to preemptively increase the resilience of a network by means of time-varying topological actuation. To do this, we focus on linear dynamical systems that are compatible with a given network, and consider policies that…
We consider a problem in which a single repairer is responsible for the maintenance and repair of a collection of machines, positioned at different locations on a network of nodes and edges. Machines deteriorate according to stochastic…
These notes are based on a short course delivered at the Summer School EUR MINT 2025 "Control, Inverse Problems and Spectral Theory", held in June 2025 in Toulouse, France. The course presents three important strategies in control theory,…
We propose a consensus based optimization algorithm with average drift (in short Ad-CBO) and provide a theoretical framework for it. In the theoretical analysis, we show that particle solutions to Ad-CBO converge to a global minimizer. In…
It is well-known that the quadratic convex reformulation (QCR) technique can speed up some general-purpose solvers such as CPLEX and Gurobi. Recently, the method of quadratic nonconvex reformulation (QNR) was proposed, which provides an…
The effective second-harmonic generation (SHG) coefficient is a crucial data that quantifies the efficiency of transforming fundamental frequency light into its second harmonic. With the help of the symmetry of nonlinear optical…