最优化与控制

We extend the convergence analysis of AdaSLS and AdaSPS in [Jiang and Stich, 2024] to the nonconvex setting, presenting a unified convergence analysis of stochastic gradient descent with adaptive Armijo line-search (AdaSLS) and Polyak…

Nonlinear optimization-based control policies, such as those those arising in nonlinear Model Predictive Control, have seen remarkable success in recent years. These policies require solving computationally demanding nonlinear optimization…

While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…

We study the regularization problem for port-Hamiltonian descriptor systems by proportional and/or derivative output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the…

This paper investigates the optimal control problem for a class of nonlinear fully coupled forward-backward stochastic difference equations (FBS$\Delta$Es). Under the convexity assumption of the control domain, we establish a variational…

This paper contributes to the compactification approach to study mean-field control problems with Poissonian common noise. To overcome the lack of compactness and continuity issues caused by common noise, we exploit the point process…

The growing scale of power systems and the increasing uncertainty introduced by renewable energy sources necessitates novel optimization techniques that are significantly faster and more accurate than existing methods. The AC Optimal Power…

Motivated by the increasing attention to overall social benefits in networked multi-agent systems, this paper investigates an optimization problem building on noncooperative games under high-level regulation, which can be formulated in a…

Advanced societies are crucially dependent on critical infrastructure networks for the reliable delivery of essential goods and services. Hence, well-founded analyses concerning disruptions are necessary to inform decisions that aim to…

We study multi-marginal optimal transport (MOT) problems where the underlying cost has a graphical structure. These graphical multi-marginal optimal transport problems have found applications in several domains including traffic flow…

In this paper, we propose an extension for semi-supervised Minimum Sum-of-Squares Clustering (MSSC) problems of MDEClust, a memetic framework based on the Differential Evolution paradigm for unsupervised clustering. In semi-supervised MSSC,…

We propose an SDP-based framework to address the stabilization of input delay systems while taking into account dissipative constraints. A key to our approach is the introduction of the concept of parameterized linear dynamical state…

Local superlinear convergence of the semismooth Newton method usually necessitates assumptions on the uniform invertibility of the utilized, generalized Jacobian matrices, such as, e.g., BD- or CD-regularity. For certain composite-type…

While Nesterov's Accelerated Gradient Descent (AGD) efficiently solves constrained problems when the constraint set $X \subseteq \mathbb{R}^n$ is simple and easy to project onto, it remains an open question whether function-constrained…

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

We develop two local energy methods for distributed parameter port-Hamiltonian (pH) systems on one-dimensional spatial domains. The methods are applied to derive a characterization of exponential stability directly in terms of the energy…

This paper presents a novel two-stage optimization framework designed to model integrated quantile functions, which leads to the formulation of a bilinear optimization problem (P). A specific instance of this framework offers a new approach…

Evaluating the reliability of machine learning classifications remains a fundamental challenge in Artificial Intelligence (AI), particularly when the target variable is multidimensional. Classification variables can be expressed by means of…

In this paper, we consider the feasibility problem, which aims to find a feasible point for the constraint set $\{x \in \mathbb{R}^n: c(x) = 0\}$ over a possibly non-regular subset $\mathcal{X} \subset \mathbb{R}^n$. Under the constraint…

This paper addresses the problem of deciding the lower-boundedness of an arbitrary real polynomial p in n variables.