最优化与控制
The rapid proliferation of distributed energy resources (DERs) and the electrification of residential loads offer significant potential for grid flexibility but pose stability challenges under static pricing regimes. Specifically, high…
Usage-based insurance (UBI) uses telematics to align premiums with risk and encourage safe driving. However, deploying these programs is challenging due to heavy-tailed claim costs, nonstationary driver behavior, and limited incentive…
An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…
Most first-order optimizers treat matrix-valued parameters as vectors, ignoring the intrinsic geometry of hidden-layer weights in neural networks. Muon addresses this mismatch by updating along the polar factor of a momentum matrix, but its…
We study the facial geometry of the homogeneous pseudo-moment cone \(\Sigma_{n,2d}^*\) and its implications for atomic decomposition of moment matrices. For fixed \(d \ge 2\), we show that if a moment matrix is formed by \(O(n^d)\)…
We study the state estimation problem for linear control systems with quadratic outputs which are locally unobservable at the equilibrium. We show that, despite this inherent lack of observability, an adversary with sensor read and write…
With the addition of large numbers of distributed energy resources (DERs) to distribution networks comes the increasing risk that their operation may violate the safety constraints of these networks. The problem considered in this paper is…
We develop a stochastic game-theoretic model for intraday dispatch of grid-scale battery energy storage systems (BESSs). We assume that each BESS operator competitively manages her state-of-charge to maximize energy arbitrage revenues,…
Gradient normalization stabilizes deep-learning optimization, and spectral normalizations are especially natural for matrix-shaped parameter blocks; Muon is the motivating example. We study an idealized deterministic, continuous-time,…
Entropic regularization provides a simple way to approximate linear programs whose constraints split into two or more tractable blocks. The resulting objectives are amenable to cyclic Kullback-Leibler (KL) Bregman projections, with…
We present a distributed framework of the Primal-Dual Hybrid Gradient (PDHG) algorithm for solving massive-scale linear programming (LP) problems. Although PDHG-based solvers demonstrate strong performance on single-node GPU architectures,…
With the advancement of modern applications, an increasing number of composite optimization problems arise whose smooth component does not possess a globally Lipschitz continuous gradient. This setting prevents the direct use of the…
It is well-known by now that the BFGS method is an effective method for minimizing nonsmooth functions. However, despite its popularity, theoretical convergence results are almost non-existent. One of the difficulties when analyzing the…
This study develops a hybrid analytical and numerical approach for dynamic user equilibrium (DUE) assignment with simultaneous route and departure time choice (RDTC) for homogeneous users. The core concept of the proposed approach is the…
This paper outlines a novel extension of the classical Pontryagin minimum (maximum) principle to stochastic optimal control problems. Contrary to the well-known stochastic Pontryagin minimum principle involving forward-backward stochastic…
We study an agency problem between a leader (the principal) seeking to design an optimal incentive scheme to a follower (the agent) to increase the value of a risky project subjected to accidents and volatility uncertainty. The agency…
We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is that it provides quantitative convergence guarantees at a much…
Dual methods are useful for distributed optimization because they allow agent-level subproblems to be solved in parallel. However, achieving primal feasibility with dual methods is a challenge; it can take many iterations to find prices…
This paper introduces a framework for solving alternating current optimal power flow (ACOPF) problems using graphics processing units (GPUs). While GPUs have demonstrated remarkable performance in various computing domains, their…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…