最优化与控制
Long-term adherence to medication is a critical factor in preventing chronic diseases, such as cardiovascular disease. To address poor adherence, physicians may recommend adherence-improving interventions; however, such interventions are…
We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when…
Over the years, computational imaging with accurate nonlinear physical models has garnered considerable interest due to its ability to achieve high-quality reconstructions. However, using such nonlinear models for reconstruction is…
We formulate and solve a variant of the quickest detection problem which features false negatives. A standard Brownian motion acquires a drift at an independent exponential random time which is not directly observable. Based on the…
Multi-robot decision-making is the process where multiple robots coordinate actions. In this paper, we aim for efficient and effective multi-robot decision-making despite the robots' limited on-board resources and the often…
We study the $L^q$-regularity of the density of barycenters of $N$ probability measures on $\mathbb{R}^d$ with respect to the $p$-Wasserstein metric ($1<p<\infty$). According to a previous result by the first author and collaborators, if…
While there is an extensive body of research analyzing policy gradient methods for discounted cumulative-reward MDPs, prior work on policy gradient methods for average-reward MDPs has been limited, with most existing results restricted to…
We propose a method for solving Karush-Kuhn-Tucker (KKT) systems that exploits block triangular submatrices by first using a Schur complement decomposition to isolate the block triangular submatrices then performing a block backsolve where…
We present a finite dimensional variational model for multi-agent path-planning in which a group of agents traverses from initial positions to a target distribution in a moving medium. The model is derived using the agent-based formulation…
We study the problem of mean-field control when the state dynamics are given by general systems of forward-backward stochastic differential equations (FBSDEs) with heterogeneous mean-field interactions. Firstly, we introduce a novel…
This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…
We study local stabilization of nonlinear control systems under explicit gain constraints on the feedback law. Using a quantitative refinement of Brockett's openness condition, we introduce the notion of a maximal continuous openness rate…
Coron established a homological obstruction to continuous feedback stabilization of nonlinear control systems $\dot{x}=f(x,u)$ with $f \in C(\Omega,\mathbb{R}^n)$ and $f(0,0)=0$, showing that local asymptotic stabilizability implies the…
We consider three key properties of Metzler and nonnegative matrices and extensions of these to classes of self-dual proper convex cones. Specifically, we study mappings that are quasi-monotone (QM) with respect to a cone $K$ and discuss…
We prove two duality descriptions of the value function for a generic stochastic optimal problem. These descriptions also hold when the diffusion is controlled, a case left open by the literature so far.
In this paper, we obtain optimality conditions for the problem with inequality, equality and closed set constraints in terms of the lower Hadamard derivative. The results are obtained applying exact penalty functions.
In this paper, we study the sub-Riemannian problem associated with contact structures on connected, simply connected, solvable, non-nilpotent, regular three-dimensional Lie groups. For these groups, the vertical component of the Hamiltonian…
We investigate the transportation problem under a Monge cost structure and derive compact formulas for optimal dual solutions based on the northwest-corner rule. As an application illustrating how these formulas yield structural insight…
We study the almost sure convergence of the Stochastic Approximation algorithm to the fixed point $x^\star$ of a nonlinear operator under a negative drift condition and a general noise sequence with finite $p$-th moment for some $p > 1$.…
We study a representation of a problem that appears in numerous transport systems: $N$ servers distributed over a given space (e.g., cars on an urban network), receive random requests from arriving users who get assigned to the closest…