最优化与控制

Stochastic non-convex non-concave optimization, formally characterized as Stochastic Variational Inequalities (SVIs), presents unique challenges due to rotational dynamics and the absence of a global merit function. While adaptive step-size…

This paper investigates leader-follower linear-quadratic stochastic graphon games, which consist of a single leader and a continuum of followers. The state equations of the followers interact through graphon coupling terms, with their…

Deployment of optimization algorithms over communication networks face challenges associated with time delays and corruptions. Fixed time delays can destabilize popular gradient-based algorithms, and this degradation is exacerbated by…

This paper presents a transferable solution method for optimal control problems with varying objectives using function encoder (FE) policies. Traditional optimization-based approaches must be re-solved whenever objectives change, resulting…

In this paper, we develop a general analysis for the fixed points of the operators defining the graph splitting methods from [SIAM J. Optim., 34 (2024), pp. 1569-1594] by Bredies, Chenchene and Naldi. We particularize it to the case where…

This paper presents a customized second-order cone programming (SOCP) solver tailored for embedded real-time optimization, which frequently arises in modern guidance and control (G&C) applications. The solver employs a practically efficient…

This paper investigates two-player ergodic nonzero-sum stochastic differential games with McKean-Vlasov dynamics. We establish a verification theorem connecting solutions of coupled Hamilton-Jacobi-Bellman (HJB) Master equations to Nash…

In this paper, we propose a deterministic diffusion-based framework for controlling the probability density of nonlinear control-affine systems, with theoretical guarantees for drift-free and linear time-invariant (LTI) dynamics. The…

Out-of-hospital cardiac arrest (OHCA) survival rates remain extremely low due to challenges in the timely accessibility of medical devices. Therefore, effective deployment of automated external defibrillators (AED) can significantly…

We propose a novel targeted exploration strategy designed specifically for uncertain linear time-invariant systems with energy-bounded disturbances, i.e., without any assumptions on the distribution of the disturbances. We use classical…

This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is…

Boolean satisfiability (SAT) is a propositional logic problem of determining whether an assignment of variables satisfies a Boolean formula. Many combinatorial optimization problems can be formulated in Boolean SAT logic -- either as k-SAT…

For the numerical solution of nonsmooth problems, sometimes it is not necessary that an exact subgradient/generalized Jacobian is at our disposal, but it suffices that a semismooth derivative, i.e., a mapping satisfying a certain…

In this paper we introduce the essential Lagrange multiplier and establish the solid mathematical foundation of constrained optimization in Hilbert spaces with sharp results on the mathematical foundation of quadratic-programming based…

This paper studies optimization of Conditional Value-at-Risk (CVaR) for Markov Decision Processes (MDPs) with finite state and action sets. It introduces the Dynamically augmented CVaR (DCVaR) risk measure and provides an algorithm for its…

We consider optimization problems containing nonconvex quadratic functions for which semidefinite programming (SDP) relaxations often yield strong bounds. We investigate linear inequalities that outer approximate the positive semidefinite…

We consider variational energies of the form \[E_H(u)=\frac12\int_\Omega H^2(\nabla u)\,dx\] defined on the Sobolev space $H^1_0(\Omega)$, where $H$ is a general seminorm. Our primary objective is to investigate optimization problems…

We study cascade coupled systems, for which our prototypical example is a 1-d heat equation coupled with a 1-d wave equation. The heat component is controlled through one boundary and the information is transmitted through another one to…

Conditional value-at-risk (CVaR) is a prominent risk measure in financial engineering, energy systems, and supply chain management. In these domains, Markov decision processes (MDPs) with a long-run CVaR criterion effectively mitigate cost…

We propose the Adaptive Levenberg-Marquardt Third-Order Newton Method (ALMTON) for unconstrained nonconvex optimization, providing the first globally convergent realization of the unregularized third-order Newton method. Unlike the standard…