最优化与控制
Air Traffic Flow Management (ATFM) traffic regulations are being increasingly used as rising demand meets persistent workforce shortages. This operational strain has amplified a critical phenomenon that we call \emph{regulation cascading}:…
When the objective has Lipschitz continuous $p$th-order derivatives, it is known that convex-concave minimax problems can be solved with $\mathcal{O}(\epsilon^{-2/(p+1)})$ $p$th-order oracle calls. This complexity upper bound was speculated…
Low-rank matrix recovery can be solved to statistical optimality by convex matrix optimization under the classical assumption of restricted isometry property (RIP). However, for large problems, the convex formulation is commonly replaced by…
The symplectic eigenvalue problem for symmetric positive-definite (spd) matrices plays a crucial role in various scientific fields, including quantum mechanics and control theory. This paper introduces a trace-penalty minimization method,…
Selecting which products to display and at what prices is a central decision in retail and e-commerce operations. In many applications, these two choices must be made jointly under limited display capacity and uncertain customer demand. In…
This paper introduces a new modeling framework for optimization under uncertainty, called Probable Event Constrained Optimization (PECO). Unlike conventional chance-constrained formulations, which only limit the probability of constraint…
This study presents a mathematical optimization framework and preliminary analysis for long-term investment planning in Puerto Rico's electric power system. We develop a high-resolution capacity expansion model to identify least-cost…
In this work we develop and analyze a semi-smooth Newton method for the general nonlinear conic programming problem. In particular, we study the problem with a generalized simplicial cone, i.e., the image of a symmetric cone under a linear…
This paper studies the integrated spacecraft routing and trajectory optimization problem for satellite servicing missions involving partial en-route propellant replenishment. Unlike terrestrial routing problems, spacecraft operate in a…
It is well known that mirror descent may diverge or cycle on merely monotone variational inequalities. In this paper, we propose \emph{Target Mirror Descent} (TMD), a unified framework that stabilizes monotone flows via a target point…
We study the approximation of the value function of deterministic optimal control problems with fixed initial state, motivated by \(N\)-body systems. In this setting, the action functional consists of local kinetic and potential terms,…
We propose a computational framework for replacing the repeated numerical solution of differential Riccati equations in finite-horizon Linear Quadratic Regulator (LQR) problems by a learned operator surrogate. Instead of solving a nonlinear…
Matrix ellipsoids provide a standard framework for representing bounded uncertainties in data-driven control. Since noise models for sequential observations are naturally represented as the Minkowski sum of multiple matrix ellipsoids,…
Rather than measuring NP search in terms of Turing-machine time, we reinterpret witness recovery as an information-acquisition process: the hidden witness is the sole source of uncertainty, and identification requires sufficient reduction…
This paper proposes a maintenance strategy for a satellite constellation that utilizes on-orbit servicing (OOS). Under this strategy, the constellation operator addresses satellite failures in two ways: by deploying new satellites and by…
In this paper we present a nonmonotone line search subgradient algorithm tailored to upper-$\mathcal{C}^2$ functions. This is a family of nonsmooth and nonconvex functions that satisfies a nonsmooth and local version of the descent lemma,…
Data informativity provides a theoretical foundation for determining whether collected data are sufficiently informative to achieve specific control objectives in data-driven control frameworks. In this study, we investigate the data…
Graph-structured data are central to many scientific and industrial applications where the goal is to optimize expensive black-box objectives defined over graph structures or node configurations -- as seen in molecular design, supply…
We present a novel universal gradient method for solving convex optimization problems. Our algorithm, Dual Averaging with Distance Adaptation (DADA), is based on the classical scheme of dual averaging and dynamically adjusts its…
We study a censored variant of the data-driven newsvendor problem, where the decision-maker must select an ordering quantity that minimizes expected overage and underage costs based only on offline censored sales data, rather than…