最优化与控制

This paper proposes a decentralized design approach of consensus protocols of multi-agent systems via a directed-spanning-tree(DST)-based linear transformation and the corresponding minimal communication links. First, the consensus problem…

We study minimax (generalized) solutions of a Cauchy problem for a (first-order) path-dependent Hamilton--Jacobi equation with co-invariant derivatives under a right-end boundary condition. Under assumptions on the Hamiltonian that are more…

Coordinating large populations of autonomous agents, such as UAV swarms or satellite constellations, poses significant computational challenges for traditional multi-agent control methods. This paper introduces a new optimization framework…

In this paper, scheduling problems of aircraft minimizing the total delays on a same runway and on dual runways are studied. In contrast to the algorithms based on mixed-integer optimization models in existing works, where the optimality…

Partially observable Markov decision processes (POMDPs) with stage duration provide a framework for approximating continuous-time behavior by scaling transition probabilities with a stage duration parameter $h \in (0,1]$. While previous…

The global Lipschitz smoothness condition underlies most convergence and complexity analyses via two key consequences: the descent lemma and the gradient Lipschitz continuity. How to study the performance of optimization algorithms in the…

Abel's classic transformation shows that any well-posed system with time-varying delay is equivalent to a parameter-varying system with fixed delay. The existence of such a parameter-varying constant delay representation then simplifies the…

An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…

We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input,…

In this paper we develop a sequential convex programming (SCP) framework for free-final-time covariance steering of nonlinear stochastic differential equations (SDEs) subject to both additive and multiplicative diffusion. We cast the…

In this paper, we study a class of misspecified variational inequalities (VIs) where both the monotone operator and nonlinear convex constraints depend on an unknown parameter learned via a secondary VI. Existing data-driven VI methods…

In this paper, we present and prove some results in multi-objective optimisation that are considered folklore. For the most part, proofs for these results exist in special cases, but they are used in more general settings since their proofs…

This paper introduces and solves a structural controllability problem for ensembles of switched linear systems. All individual systems in the ensemble are sparse and governed by the same sparsity pattern, and undergo switching among…

Generalized Disjunctive Programming (GDP) provides a natural framework for optimization models that combine logical decisions with nonlinear constraints. The Hull Reformulation (HR) is attractive because it yields tight continuous…

One important question in the theory of lattices is to detect a shortest vector: given a norm and a lattice, what is the smallest norm attained by a non-zero vector contained in the lattice? We focus on the infinity norm and work with…

We study the problem of joint optimization involving coding and control policies for a controlled Markovian sytem over a finite-rate noiseless communication channel. While structural results on the optimal encoding and control have been…

Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over…

Motivated by widespread electrification targets, this paper studies an Electric Vehicle Routing Problem with Time Windows and Nonlinear Charging (EVRPTWNL) that jointly optimizes routing-scheduling decisions and charging decisions given…

In this work, we present a new deterministic partition-based global optimization algorithm, HALO (Hybrid Adaptive Lipschitzian Optimization), which uses estimates of the local Lipschitz constants associated with different sub-regions of the…

The purpose of these notes is to provide background on understanding the primal-dual algorithm of Chambolle and Pock [1] for imaging scientists. The presentation focuses on providing intuition and an algorithmic system that is amenable to…