Research
Research
Research
Research
15,708+ open-access research outputs.
This paper studies data-driven approaches to the continuous-time linear quadratic regulator (LQR) problem based on two existing parameterizations, namely a closed-loop (CL) parameterization from behav…
We study the extremal energy problem for complex unit gain graphs whose underlying graph is the dumbbell graph $D_{r,s,\ell}$. An explicit expression of its characteristic polynomial is derived in ter…
We construct the multilevel correlation kernel for the rising GUE eigenvalue process starting from a fixed initial configuration $x^{(m)}$, and show that it converges on short time scales (as quickly …
In finance, portfolio management is a traditional yet difficult problem that has drawn attention from practitioners and researchers for many years. However, there are still difficult technological pro…
Motivated by an optimal-matching problem (Leighton-Shor) and the random-field Ising model (Aizenman-Wehr, Ding-Wirth), we consider a variational problem for graphs in $1+1$ dimension maximizing an act…
Bayesian online learning provides a coherent framework for sequential inference. However, its theoretical understanding remains limited, particularly in the one-pass setting. Existing theoretical guar…
We propose a regularized Hessian-free Newton-type method for minimizing smooth convex functions with Lipschitz continuous Hessians. The algorithm constructs an approximate Hessian by finite difference…
Across science and engineering, mean-field methods have been a powerful and versatile approach for the analysis of systems of many interacting elements. However, common arguments used to characterize …
This paper is a continuation work of Ren et al. (2026) aiming to further devise q-learning algorithms for mean-field control (MFC) with controlled common noise. Based on the relaxed control formulatio…
This paper investigates the continuous-time counterpart of the Q-function for entropy-regularized mean-field control (MFC) with controlled common noise, coined as q-function by Jia and Zhou (2023) in …
We prove that the directed five-dimensional torus $D_5(m) = \operatorname{Cay}((\mathbb{Z}_m)^5, \{e_0, e_1, e_2, e_3, e_4\})$ has a Hamilton decomposition for every odd integer $m \geq 3$. This is th…
Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide suffici…
The Alternating Direction Method of Multipliers (ADMM) is a widely used method for structured convex optimization, and its practical performance depends strongly on the choice of penalty and relaxatio…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). I…
In this work, we study optimization specified only through a comparison oracle: given two points, it reports which one is preferred. We call it function-free optimization because we do not assume acce…
Hill functions, dominant in gene regulatory network modeling, carry fundamental limitations: at non-integer cooperativity exponents, routine when fitting dose-response data, derivatives diverge at the…
Existing methods for learning Stackelberg equilibria typically assume that the followers' (variational, generalized) Nash equilibrium is unique. However, in the presence of multiple equilibria, withou…
We study the optimization of (strongly) quasar-convex functions, a class that arises naturally in many machine learning and data science applications due to its favorable properties. The fundamental p…
Power grid infrastructure is an increasingly significant source of wildfire ignitions and poses severe risks to communities in fire-prone regions. Public Safety Power Shutoffs (PSPS) have emerged as a…
We analyze a three-dimensional discontinuous piecewise linear system \(Z=(X,Y)\) whose switching manifold \(\Sigma\) contains visible-visible two-fold intersection lines. Assuming that the matrices \(…
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