最优化与控制

In this review, we offer a comprehensive survey of emerging techniques in gradient-based optimization, with a particular emphasis on the interplay between ordinary differential equation (ODE) perspectives and their extensions into discrete…

We propose a derivative-free matrix conjugate-subgradient method for unconstrained nonsmooth optimization of locally Lipschitz functions. The method constructs discrete gradients using only function values and forms a finite sampled model…

When datasets contain outliers, robust regression is a well-established alternative to Ordinary Least Squares. A commonly employed robust estimator is Least Trimmed Squares (LTS), which computes the regression coefficients from a subset of…

We prove that the Sinkhorn algorithm converges at the rate of $O(1/k)$ in $\ell_1$-norm marginal error and in joint relative entropy, which is known to be sharp in the asymptotically scalable case. The proof is based on examining the…

We develop a second-order sensitivity theory for the efficient solution map \(S\) of a parametric vector optimization problem \(\min_C f(p,x)\) subject to \(x\in H(p)\). The main point is the passage from efficient values to efficient…

In this paper, we consider distributed parameter estimation with binary observations under measurement-side tampering: each node observes a thresholded output whose label may be flipped and exchanges information over a communication graph.…

We study a mean-field optimal control problem for a consensus (high-dimensional Kuramoto-type) dynamics with diffusion on the unit sphere. The control acts through a prescribed drift field and an interaction gain, and the cost functional is…

Robust Markov decision processes provide a principled framework for protecting sequential decision-making against transition-law misspecification and have attracted substantial recent research interest. As in non-robust stochastic optimal…

In this work, we propose a robust Sparse Identification of Nonlinear Dynamics (SINDy) pipeline for handling datasets corrupted by noise and outliers. The method decouples outlier filtering from sparse regression by combining Iterative Least…

Systems defined by linear and complementarity constraints (SLCCs) arise frequently in engineering, economics, and other related fields. They also appear in the optimality conditions of many challenging optimization models, such as bilinear…

In this article, we introduce a new noise model for data-driven control. The model can be interpreted as a generalization of a Frobenius norm bound on the matrix of noise samples. For instantaneously bounded noise, the proposed model…

Scalar objective functions are required when a multi-criteria optimization problem must yield a single preferred design rather than only a Pareto set. The choice of scalarization influences which compromise is selected, how preference…

We analyze Bregman ADMM for nonconvex linearly constrained problems under two-sided relative smoothness, a condition that replaces the standard Lipschitz gradient assumption with a Hessian comparison relative to a Bregman kernel. This…

We study the optimal complexity of first-order methods under the $\alpha$-Polyak-Lojasiewicz condition with $\alpha\in[1,2)$. This condition bounds the suboptimality gap by a power $\alpha$ of the gradient norm; $\alpha=2$ recovers the…

This paper studies the mean field game of mutual holding proposed by Djete and Touzi(AAP, 2024), and consider the case where the interactions among agents are described by a graphon. We adopt the formulation on the enlarged space which is…

In this paper, we study nonconvex equality-constrained optimization problems in which only stochastic first-order approximations of the objective and constraint functions are available. Owing to the stochasticity in both objective and…

Construction of Earth-Moon transfers is the basis of missions to explore the Moon and cislunar space. The traditional grid search method suffers from a relatively low convergence rate and computational efficiency, mainly focusing on the…

We study a class of nonconvex cardinality-constrained optimization problems arising in sparse learning. These problems are NP-hard due to the combinatorial nature of sparsity constraints. We introduce a Reservoir Zero-Coordinatewise…

We study the local controllability near zero of the Burgers equation with a scalar control and a fixed space-dependent source profile, in the case where the linearized system fails to be controllable and a second-order analysis is therefore…

In this paper, we study a broad class of structured monotone inclusion problems in real Hilbert spaces. We propose a novel primal-dual splitting algorithm for solving such inclusions, which accommodates multiple monotone operators and…