最优化与控制

A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic…

This paper develops a joint spectral radius (JSR) framework for analyzing rank-one deflated Q-value iteration (Q-VI) in discounted Markov decision process control. Focusing on an all-ones residual correction, we interpret the resulting…

The Frank-Wolfe algorithm achieves a convergence rate of $\mathcal{O}(1/T)$ for smooth convex optimization over compact convex domains, accelerating to $\mathcal{O}(1/T^2)$ when both the objective and the feasible set are strongly convex.…

We consider Decision-Focused Federated Learning (DFFL), a predict-then-optimize setting in which multiple clients collaboratively train predictive models for downstream linear optimization problems without exchanging raw data. Besides the…

We propose a Parameter-Free Universal Gradient Sliding (PFUGS) algorithm for computing an approximate solution to the convex composite optimization $\min_{x\in X} \{f(x) + g(x)\}$, where $f$ has $(M_\nu,\nu)$-H\"older continuous subgradient…

Extreme weather events, like flooding, disrupt urban transportation networks by reducing speeds and capacities, and by closing roadways. These hazards create regime-dependent uncertainty in link performance and travel-time distribution…

In this paper, an input-to-state Lyapunov function for the RMSProp optimization algorithm is introduced. Global asymptotic stability of the RMSProp algorithm for constant step sizes and robustness properties with respect to arbitrary…

Controllability scores provide control-theoretic centrality measures that quantify the relative importance of state nodes in networked dynamical systems. We establish a structural connection between finite-time controllability scoring and…

We study spatial decay properties of sensitivities in a nonlinear optimal control problem with a graph-structured interaction topology. For a problem with nonlinear decoupled dynamics and quadratic cost, we show that a perturbation of the…

Optimization under heavy-tailed noise has become popular recently, since it better fits many modern machine learning tasks, as captured by empirical observations. Concretely, instead of a finite second moment on gradient noise, a bounded…

This paper is concerned with performance analysis and pole selection problem in identifying linear time-invariant (LTI) systems using orthogonal basis functions (OBFs), a system identification approach that consists of solving least-squares…

In this paper, we propose objective-function-free (OFF) variants of the proximal Newton method for nonconvex composite optimization problems and the regularized Newton method for unconstrained optimization problems, respectively, using…

The Brunovsky canonical form provides sparse structural representations that are beneficial for computational optimal control, yet existing methods fail to compute it reliably. We propose a technique that produces Brunovsky transformations…

We formalise decompression planning as an optimal control problem with gas feasibility windows (ppO$_2$, END), affine ceilings, and convex penalties in normalised oversaturation. The depth trajectory is constrained to be a monotone ascent,…

We consider mean field social optimization in nonlinear diffusion models. By dynamic programming with a representative agent employing cooperative optimizer selection, we derive a new Hamilton--Jacobi--Bellman (HJB) equation to be called…

Iteration complexities for optimizing smooth functions with first-order algorithms are typically stated in terms of a global Lipschitz constant of the gradient, and near-optimal results are then achieved using fixed step sizes. But many…

We propose an enhancement to Benders decomposition (BD) that generates valid inequalities for the convex hull of the Benders reformulation, addressing the limitation that classical BD cuts are typically tight only for the continuous…

The mathematical program with equilibrium constraints (MPEC) is a powerful yet challenging class of constrained optimization problems, where the constraints are characterized by a parametrized variational inequality (VI) problem. While…

We analyze a sequential quadratic programming algorithm for solving a class of abstract optimization problems. Assuming that the initial point is in an $L^2$ neighborhood of a local solution that satisfies no-gap second-order sufficient…

Constrained decentralized team problem formulations are good models for many cooperative multi-agent systems. Constraints necessitate randomization when solving for optimal solutions -- past results show that joint randomization in the team…