最优化与控制

This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…

As a foundation for optimization, convexity is useful beyond the classical settings of Euclidean and Hilbert space. The broader arena of nonpositively curved metric spaces, which includes manifolds like hyperbolic space, as well as metric…

We consider a minimization problem of the form $P(\varphi, g, h):$ $$\min\left\{f(x):= \varphi(x) + g(x) - h(x) \colon x \in \mathbb{R}^n\right\},$$ where $\varphi$ is a differentiable function and $g,$ $h$ are convex functions, and…

Let $f:2^{E} \rightarrow \mathbb{Z}_+$ be a submodular function on a ground set $E = [n]$, and let $P(f)$ denote its extended polymatroid. Given a direction $d \in \mathbb{Z}^n$ with at least one positive entry, the line search problem is…

Stability of economic model predictive control can be proven under the assumption that a strict dissipativity condition holds. This assumption has a clear interpretation in terms of the so-called rotated stage cost, which must have its…

Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…

Distributed optimization has gained substantial interest in recent years due to its wide applications in machine learning. However, most of existing algorithms are designed for Euclidean spaces, leaving composite optimization on Riemannian…

The autocovariance least squares (ALS) method is a computationally efficient approach for estimating noise covariances in Kalman filters without requiring specific noise models. However, conventional ALS and its variants rely on the classic…

This paper investigates the \emph{Wiring Diagram Problem} (WDP), a three-dimensional layout design problem arising in industrial applications such as cable harness design and pipeline routing in constrained environments. In these settings,…

Classical stability theory for stochastic programming relies on the Wasserstein-Fortet-Mourier duality, which requires the ground cost to be a distance. When using problem-dependent costs instead of metrics, this duality no longer yields…

In this paper, we study the finite-horizon problem of an economic agent's optimal consumption, investment, and job-switching decisions. The key new feature of our model is that the job-switching cost is time-varying. This extension leads to…

Funds at large portfolio management firms may consist of many portfolio managers (PMs), each managing a portion of the fund and optimizing a distinct objective. Although the PMs determine their trades independently, the trade lists may be…

Along with the rapid development of new urban mobility options like ride-sharing over the past decade, on-demand micro-transit services stand out as a middle ground, bridging the gap between fixed-line mass transit and single-request…

This paper investigates the distributed stochastic nonconvex and nonsmooth composite optimization problem. Existing stochastic typically rely on uniform step size strictly bounded by global network parameters, such as the maximum node…

Federated Composite Optimization (FCO) has emerged as a promising framework for training models with structural constraints (e.g., sparsity) in distributed edge networks. However, simultaneously achieving communication efficiency and…

We study the problem of online tracking in unknown nonlinear dynamical systems, where only short-horizon predictions of future target states are available. This setting arises in practical scenarios where full future information and exact…

In this paper, we study the problem of learning to bid in repeated first-price auctions with budget constraints. In each period, the decision maker needs to submit a bid to win the auction and maximize the total collected reward, subject to…

This paper first presents a detailed implementation of Newton's method on the indefinite Stiefel manifold. To this end, an intensive analysis of the second-order geometry of the manifold is performed. Specifically, given the two types of…

For a generic discrete-time algorithm (DTA): $z^+=g(z,s)$, where $s$ is the step size, Lu (Math. Program., 194(1):1061--1112, 2022) proposed an $O(s^r)$-resolution ordinary differential equation (ODE) framework based on the backward error…

Nesterov's accelerated gradient descent method (AGD) is a seminal deterministic first-order method known to achieve the optimal order of iteration complexity for solving convex smooth optimization problems. Two distinct sequences of…