最优化与控制

AI data centers (AIDCs) are rapidly increasing electricity demand and associated CO2 emissions, yet they also generate continuous low-grade waste heat. Here, we assess whether this heat can be upgraded by heat pumps to drive direct air…

In this paper, we consider infinite-horizon linear-quadratic cooperative differential games with output feedback information structure. We first demonstrate that, under output feedback information structure, computing Pareto optimal…

In this paper, we study an infinite horizon non-autonomous stochastic recursive differential game. To this end, we first establish well-posedness and stability results for BSDEs with a time-dependent discount factor and a possibly unbounded…

We propose Adam-SHANG, a Lyapunov-guided Adam-type method that couples momentum, adaptive preconditioning, and a curvature-aware correction through a more stable lagged-preconditioner update. For stochastic smooth convex optimization, we…

This work is about ME, the Method of Ellipcenters. ME was recently introduced by these very authors as a first order accelerated scheme for unconstrained minimization. Its iterates are all centers of ellipses carefully designed to somehow…

We study three quadratic models in model-based derivative-free optimization: the minimum norm (MN), minimum Frobenius norm (MFN), and quadratic generalized simplex derivative (QS) models. Despite their widespread use, their approximation…

This paper studies indefinite stochastic linear-quadratic (LQ) optimal control for jump-diffusion systems with random coefficients. We construct an algebraic inverse flow from the zero-control base system, extract the semimartingale kernel…

Large language models (LLMs) are pretrained by minimizing the cross-entropy loss for next-token prediction. In this paper, we study whether this optimization strategy can induce geometric structure in the learned model weights and context…

This paper addresses the class of continuous-time nonlinear programming problems with equality and inequality constraints. The paper presents necessary optimality conditions of the sequential form. To be more precise, a sequence of…

Newton-type methods are typically analyzed under Lipschitz continuity of the Hessian, an assumption that can fail for objectives with higher-order or polynomial growth. We introduce a class of nonlinearly preconditioned Newton methods that…

We develop a new interior-point algorithm for solving multiconic optimization problems using the parabolic target space approach. The feasible cone in these problems is composed as a direct product of many small-dimensional cones. Our…

We study the doubly nonnegative (DNN) relaxation of the standard quadratic optimization problem \[ \min\{x^\top Qx:\ x\in\Delta^{n-1}\},\qquad \Delta^{n-1}:=\{x\in\mathbb{R}_+^n:\ \mathbb{1}^\top x=1\}, \] for random symmetric matrices with…

Identifying robust designs for multi-energy systems is computationally challenging. As rigorous approaches are often computationally intractable, heuristics are employed to generate candidate designs. One example is the feasibility…

This paper introduces computationally efficient methods for synthesizing explicit piecewise affine (PWA) feedback laws for nonlinear discrete-time systems, ensuring robustness and performance guarantees. The approach proceeds by optimizing…

In this paper, we propose a primal-dual splitting algorithm for a broad class of structured composite monotone inclusions that involve finitely many set-valued operators, compositions of set-valued operators with bounded linear operators,…

This paper develops a unified perspective on several optimal control formulations through the lens of Kullback-Leibler (KL) regularization. We propose a central problem that separates the KL penalties on policies and transitions with…

An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…

This paper studies a class of monotone inclusion problems in a real Hilbert space involving the sum of three operators, where two are maximal monotone and the third is cocoercive. The Davis--Yin three-operator splitting method extends the…

A wide range of optimization problems can often be written in terms of generalized convex functions (GCFs). When this structure is present, it can convert certain nested bilevel objectives into single-level problems amenable to standard…

Unconstrained binary integer programming (UBIP) is a challenging optimization problem due to the presence of binary variables. To address the challenge, we introduce a novel class of functions named sharp-peak functions (SPFs), which…