最优化与控制

The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{\Delta,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $\Delta$ and…

Existing methods for nonconvex bilevel optimization (NBO) require prior knowledge of first- and second-order problem-specific parameters (e.g., Lipschitz constants and the Polyak-{\L}ojasiewicz (P{\L}) parameters) to set step sizes, a…

We study affine control systems on smooth manifolds and their complete lifts to the tangent bundle, providing an explicit geometric description of the solutions of the lifted system. We show that, although controllability of the complete…

We develop and analyze a single-loop algorithm for minimizing the sum of a Lipschitz differentiable function $f$, a prox-friendly proper closed function $g$ (with a closed domain on which $g$ is continuous) and the composition of another…

This paper studies the policy mirror descent (PMD) method, which is a general policy optimization framework in reinforcement learning and can cover a wide range of policy gradient methods by specifying difference mirror maps. Existing…

We study the Reflect-Reflect-Relax (RRR) algorithm in its small-step (flow-limit) regime. In the smooth transversal setting, we show that the transverse dynamics form a hyperbolic sink, yielding exponential decay of a natural gap measure.…

Cooperative collision avoidance between robots, or `agents,' in swarm operations remains an open challenge. Assuming a decentralized architecture, each agent is responsible for making its own decisions and choosing its control actions. Most…

This work proposes a unified control architecture that couples a Reinforcement Learning (RL)-driven controller with a disturbance-rejection Extended State Observer (ESO), complemented by an Event-Triggered Mechanism (ETM) to limit…

It is an old idea to use gradient flows or time-discretized variants thereof as methods for solving minimization problems. In some applications, for example in machine learning contexts, it is important to know that for generic initial…

We consider the central role of improving directions in solution methods for mixed integer bilevel linear optimization problems (MIBLPs). Current state-of-the-art methods for solving MIBLPs employ the branch-and-cut framework originally…

In this study, we consider a multi-pursuer single-evader quantitative pursuit-evasion game with payoff function that includes only the terminal cost. The terminal cost is a function related only to the terminal position of the evader. This…

A fundamental theorem of linear programming states that a feasible linear program is solvable if and only if its objective function is copositive with respect to the recession cone of its feasible set. This paper demonstrates that this…

In this paper, we establish a distributed functional optimization (DFO) theory over time-varying networks. The vast majority of existing distributed optimization theories are developed based on Euclidean decision variables. However, for…

The objective of this paper is to investigate the connection between penalty functions from stochastic optimal control, convex semigroups from analysis and convex expectations from probability theory. Our main result provides a one-to-one…

This paper concerns the problem of reachability of a given state for a multiagent control system in $\mathbb{R}^d$. In such a system, at every time each agent can choose his/her velocity which depends both on his/her position and on the…

Green hydrogen has multiple use cases and is produced from renewable energy, such as solar or wind energy. It can be stored in large quantities, decoupling renewable energy generation from its use, and is therefore considered essential for…

This paper investigates the approximate controllability of linear fractional impulsive evolution equations in Hilbert spaces. The system under consideration involves the Caputo fractional derivative of order $0<\alpha\leq 1$, a closed…

We introduce the GEneralized Newton Inexact Operator Splitting solver (GeNIOS) for large-scale convex optimization. GeNIOS speeds up ADMM by approximately solving approximate subproblems: it uses a second-order approximation to the most…

The paper develops a second-order time-domain moment matching framework for the structure-preserving model reduction of second-order dynamical systems of high dimension, avoiding the first-order double-sized equivalent system. The moments…

Closed-loop optimal control design for high-dimensional nonlinear systems has been a long-standing challenge. Traditional methods, such as solving the associated Hamilton-Jacobi-Bellman equation, suffer from the curse of dimensionality.…