最优化与控制
We study optimization problems on Hadamard manifolds, motivated by recent advances in geometric approaches to optimization on curved spaces, particularly those involving the structure of Busemann functions. We introduce a projection based…
This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" +…
McKean-Vlasov (MKV) systems provide a unifying framework for recent state-of-the-art particlebased methods for global optimization. While individual particles follow stochastic trajectories, the probability law evolves deterministically in…
Beck and Teboulle's FISTA for finding the minimizer of the sum of two convex functions is one of the most important algorithms of the past decades. While function value convergence of the iterates was known, the actual convergence of the…
Zeroth-order optimization (ZO) has been a powerful framework for solving black-box problems, which estimates gradients using zeroth-order data to update variables iteratively. The practical applicability of ZO critically depends on the…
Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents a significant computational challenge, motivating the development of machine learning-based…
We introduce AutoLyap, a software suite that assists with Lyapunov analyses of a wide class of first-order methods for structured optimization and inclusion problems. Lyapunov analyses are structured proof patterns, with historical roots in…
In this paper, we study a maximization problem on real sequences. More precisely, for a given sequence, we are interested in computing the supremum of the sequence and an index for which the associated term is maximal. We propose a general…
Symmetric cone programming covers a broad class of convex optimization problems, including linear programming, second-order cone programming, and semidefinite programming. Although the augmented Lagrangian method (ALM) is well-suited for…
This paper considers the stochastic convex composite optimization problem and presents multi-cut stochastic approximation (SA) methods for solving it, whose models in expectation overestimate its objective function. The multi-cut model…
We introduce symmetric cone games (SCGs), a broad class of multi-player games where each player's strategy lies in a generalized simplex (the trace-one slice of a symmetric cone). This framework unifies a wide spectrum of settings,…
We present a multi-agent and mean-field formulation of a game between investors who receive private signals informing their investment decisions and who interact through relative performance concerns. A key tool in our model is a Poisson…
This paper focuses on the data-driven optimal structured controller design for discrete-time linear time-invariant (LTI) systems, considering both the $H_2$ performance and the $H_\infty$ performance. Specifically, we consider three…
We consider the problem of minimizing a smooth and convex function over the $n$-dimensional spectrahedron -- the set of real symmetric $n\times n$ positive semidefinite matrices with unit trace, which underlies numerous applications in…
We establish a discrete operator--theoretic framework for the analysis of implicit Euler and Lie--Trotter splitting schemes for delay differential equations (DDEs). Both schemes are formulated in terms of discrete resolvent operators acting…
Distributed optimization problems usually face inexact communication issues induced by channel noise, communication quantization or differential privacy protection. Most existing algorithms need a two-timescale setting of the stepsize of…
In this paper, we extend two classes of functions involved in asymptotic stability analyses. The goal of this extension is to study a maximization problem on the reachable values of a discrete-time dynamical system. This specific…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
This paper studies sample average approximation (SAA) in solving convex or strongly convex stochastic programming (SP) problems. In estimating SAA's sample efficiency, the state-of-the-art sample complexity bounds entail metric entropy…
Motivated by online dating platforms, we study the problem of selecting which subset of profiles to display to each user in each period. Users observe the profiles set by the platform, decide which of them to like, and a match occurs if and…