最优化与控制
Robust control of complex engineered and biological systems hinges on the integration of feedforward and feedback mechanisms. This is exemplified in neural motor control, where feedforward muscle co-contraction complements sensory-driven…
In recent years, nonconvex minimax problems have attracted significant attention due to their broad applications in machine learning, including generative adversarial networks, robust optimization and adversarial training. Most existing…
We obtain a probabilistic solution to linear-quadratic optimal control problems with state constraints. Given a closed set $\mathcal{D}\subseteq [0,T]\times\mathbb{R}^d$, a diffusion $X$ in $\mathbb{R}^d$ must be linearly controlled in…
Mixed H2/H-infinity control balances performance and robustness by minimizing an H2 cost bound subject to an H-infinity constraint. However, classical Riccati/LMI solutions offer limited insight into the nonconvex optimization landscape and…
Let X be an irreducible complex affine algebraic variety defined over $\mathbb{R}$, equipped with a faithful action of a finite group G, and let Y = X // G denote the categorical quotient with projection $\pi$. We study the geometry of the…
The Muon optimizer has recently attracted attention due to its orthogonalized first-order updates, and a deeper theoretical understanding of its convergence behavior is essential for guiding practical applications; however, existing…
We propose a distributed accelerated primal-dual method with backtracking (D-APDB) for cooperative multi-agent constrained consensus optimization problems over an undirected network of agents, where only those agents connected by an edge…
We propose FlexQP, an always-feasible convex quadratic programming (QP) solver based on an $\ell_1$ elastic relaxation of the QP constraints. If the original constraints are feasible, FlexQP provably recovers the optimal solution. If the…
This paper focuses on decentralized composite optimization over networks without a central coordinator. We propose a novel decentralized symmetric ADMM algorithm that incorporates multiple communication rounds within each iteration, derived…
In this work, we use the matrix formulation of the Permutation Flowshop Scheduling Problem with makespan minimization to derive an upper bound and a general framework for obtaining lower bounds. The proposed framework involves solving a…
This paper is devoted to the class of paraconvex functions and presents some of its fundamental properties, characterization, and examples that can be used for their recognition and optimization. Next, the convergence analysis of the…
We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…
We study a pair of budget- and performance-constrained weak-submodular maximization problems. For computational efficiency, we explore the use of stochastic greedy algorithms which limit the search space via random sampling instead of the…
Control Lyapunov Functions (CLFs) have been extensively used in the control community. A well-known drawback is the absence of a systematic way to construct CLFs for general nonlinear systems, and the problem can become more complex with…
In this paper, we study zeroth-order algorithms for nonconvex minimax problems with coupled linear constraints under the deterministic and stochastic settings, which have attracted wide attention in machine learning, signal processing and…
Ground Delay Programs (GDPs) mitigate demand-capacity imbalances by holding flights on the ground when an airport's arrival capacity is reduced, thereby reducing costly airborne holding. A central challenge is that day-to-day…
We develop and analyze the Generalized Multiplicative Gradient (GMG) method for solving a class of convex optimization problems over symmetric cones, where the objective function does not have Lipschitz gradient over the feasible region.…
Privacy in multi-agent control is receiving increased attention, though often a networked system and privacy protections are designed separately, which can harm performance. Therefore, this paper presents a co-design framework for networks…
This paper studies maintenance optimization for a two-component system under mixed observability. Component~$U_1$ is fully monitored, whereas component~$U_2$ is only partially observable due to sensing limitations. The system exhibits…
We study infinite-horizon Markov decision processes (MDPs) where the decision maker evaluates each of her strategies by aggregating the infinite stream of expected stage-rewards. The crucial feature of our approach is that the aggregation…