最优化与控制

We propose Nesterov acceleration with Operator Decomposition (NOD), which extends Nesterov's accelerated gradient descent (NAG) from smooth strongly convex optimization to the broader setting of strongly monotone, Lipschitz operators. The…

We study the input-to-state stability (ISS) of boundary control systems allowing for infinitely many boundary couplings. Using semigroup perturbation theory and the theory of positive linear operators on Banach lattices, we derive a…

Inverse problems in scientific computing often require optimization over infinite-dimensional Hilbert spaces. A commonly used solver in such settings is stochastic gradient descent (SGD), where gradients are approximated using randomly…

Research on multi-objective combinatorial optimization and on the Cutting Stock Problem (CSP) has been widely developed over the years. In contrast, the multi-objective Cutting Stock Problem has received limited attention and has been…

We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…

We study a catching-up algorithm for a class of differential inclusions driven by maximal monotone operators with continuous perturbations. Using a decomposition of the monotone operator into the closed convex hull of its single-valued part…

We study whether second-order systems can be made to behave like prescribed first-order dynamical systems through feedback control. More precisely, we study whether prescribed vector fields on compact smooth manifolds, viewed geometrically…

We study the convergence of the last iterate (i.e., the $(N+1)$-th iterate) of the AdaGrad method. Although AdaGrad -- an adaptive subgradient method -- underpins a wide class of algorithms, most existing convergence analyses focus on…

We investigate the robust Stackelberg null controllability of a one-dimensional forward linear stochastic Kuramoto--Sivashinsky--Korteweg--de Vries (KS--KdV) equation. The control framework is formulated as a hierarchical Stackelberg game…

In this paper, we propose a unified compression algorithm for distributed nonconvex opitmization with both the locally- and globally-bounded communication compressors, including 1-bit compressors, saturating quantizers, and the…

This paper focuses on the discrete-time backward stochastic linear quadratic (BSLQ) optimal control problem with nonhomogeneous system terms and cost function cross terms. The terminal constraint of such systems distinguishes it from…

In this paper, we develop a distributed algorithm for solving a class of distributed convex optimization problems where the local objective functions can be a general nonsmooth function, and all equalities and inequalities are network-wide…

From adversarial robustness to multi-agent learning, many machine learning tasks can be cast as finite-sum min-max optimization or, more generally, as variational inequality problems (VIPs). Owing to their simplicity and scalability,…

In this paper, we study the maximum entropy sampling problem (MESP) and its variants. MESP seeks to identify a small subset of variables that maximizes the determinant of a covariance submatrix, and is a fundamental model in optimal…

Hub location problems are central to optimizing logistics, telecommunications, and transportation networks by consolidating flows through strategically placed hubs. While existing models assume symmetric allocation, where hubs handle…

We study policy iteration (PI) for deterministic infinite-horizon discounted optimal control problems, whose value function is characterized by a stationary Hamilton--Jacobi--Bellman (HJB) equation. At the PDE level, PI is fundamentally…

Byzantine-robust distributed optimization relies on robust aggregation rules to mitigate the influence of malicious Byzantine workers. Despite the proliferation of such rules, a unified convergence analysis framework that accommodates…

Direct numerical simulation of dense rigid body suspensions poses significant computational challenges. A popular approach to resolve collisions necessitates solving a linear complementary problem (LCP) per time step. Each matrix vector…

Managing stock efficiently remains a core issue in modern logistics, where companies must reconcile cost efficiency with dependable service despite unpredictable market conditions. Conventional models often overlook the direct connection…

Time-varying optimization is fundamental to decision-making in dynamic environments, where objectives evolve over time due to exogenous signals or data streams. However, algorithms designed for static problems yield suboptimal decisions in…