最优化与控制
We study the vanishing-regularization limit of entropically regularized optimal transport (EOT) for the Euclidean distance cost $c(x,y)=\|x-y\|$ in dimension $d>1$. We develop a comprehensive variational convergence framework that entails…
It is well known that estimating the expectation of any given bounded random variable with values in $[-B, B]$ has a sample complexity of $\mathrm{O}(B^2/\epsilon^2)$ that is independent of the underlying probability measure. We show that…
We study a stochastic variant of the Team Orienteering Problem with lognormal travel times and an all-or-nothing reward policy, under which the reward of a route is lost if its travel time exceeds the available budget. We propose a…
We investigate the stabilisation of nominally linear-affine switched systems with uncertain Lipschitz nonlinearities under dwell-time constraints, using a sampled-data switching law based on a state observer. We design the switching law…
Optimal control for fully observed diffusion processes is well established and has led to numerous numerical implementations based on, for example, Bellman's principle, model free reinforcement learning, Pontryagin's maximum principle, and…
Accurate electroencephalography (EEG) and magnetoencephalography (MEG) source localization and reconstruction are essential for understanding brain function, yet remain challenging because the underlying EEG/MEG inverse problem is…
Basis pursuit is the problem of finding a vector with smallest $\ell_1$-norm among the solutions of a given linear system of equations. It is a well-known convex relaxation of the sparse affine feasibility problem, where sparse solutions to…
We present an improvement of a recent funnel controller design for uncertain nonlinear multi-input, multi-output systems modeled by higher order functional differential equations in the presence of input constraints. The objective is to…
In this paper, we present an efficient algorithm for solving a linear optimization problem with entropic constraints, a class of problems that arises in game theory and information theory. Our analysis distinguishes between the cases of…
The Lov\'asz theta function is a semidefinite programming (SDP) relaxation for the maximum weighted stable set problem, which is tight for perfect graphs. However, even for perfect graphs, there is no known rounding method guaranteed to…
Fej\'er monotonicity is a well-established property often observed in sequences generated by optimization algorithms. In this paper, we study an extension of this property, called Fej\'er* monotonicity, which was initially proposed in [SIAM…
Bilevel optimization reveals the inner structure of otherwise oblique optimization problems, such as hyperparameter tuning, neural architecture search, and meta-learning. A common goal in bilevel optimization is to minimize a…
We study finite-horizon quadratic control of linear systems with bilinear observations, in which the control input affects not only the state dynamics but also the partial observations of the state. In this setting, the separation principle…
In this article, we develop an efficient algorithm based on three special variants of the nonlinear conjugate gradient method, namely, the Polak--Ribiere--Polyak, Hestenes--Stiefel, and Liu--Story schemes for computing Pareto critical…
Coordinating production and material transfers is increasingly important in modern manufacturing systems equipped with mobile transfer robots, known as transbots. This study considers a flexible job shop environment in which heterogeneous…
In this paper we study continuum-marginal optimal transport. Given a time-continuous family of probability marginals, the problem is to recover the minimum-energy velocity field whose flow reproduces every marginal. This problem is the…
We establish the approximate controllability in $L^2$ for the nonlinear Benjamin-Ono equation on torus via two-dimensional control input. Our proof is based on adaptations of geometric control approach introduced by Agrachev and Sarychev.…
We present a trust-region-based adaptive finite-element algorithm for numerically solving a class of nonsmooth PDE-constrained optimization problems that includes problems with sparsifying regularizers and convex constraints. In particular,…
This paper studies economic model predictive Control (EMPC) schemes, where the stage cost depends only on control inputs. Such problems arise in applications like water distribution networks and differ from standard EMPC since multiple…
Fully decentralized Muon is difficult because its nonlinear matrix-sign operator does not commute with linear gossip averaging. This makes decentralized Muon a structural design problem: in designing the algorithm, one must distinguish…