最优化与控制

Open-weight foundation models can be fine-tuned for harmful purposes after release, yet no existing training resistance methods provide theoretical guarantees. Treating these interventions as convergence-rate control problems allows us to…

Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for…

We study the i.i.d. $k$-selection prophet inequality problem, where a decision-maker sequentially observes $n$ independent nonnegative rewards and may accept at most $k$ of them without knowledge of future realizations. The objective is to…

Many biological systems are observed through heterogeneous modalities, requiring transport models that couple dynamics across spaces while allowing mass variation. To address this challenge, we introduce Unbalanced Synchronized Optimal…

Denote the maximum sos rank of $m \times n$ sum of squares (SOS) biquadratic forms by $BSR(m, n)$. In this paper, we show that $BSR(m, n) \ge z(m, n)$ and conjecture that $BSR(m, n) = z(m, n)$, where $z(m, n)$ is the Zarankiewicz number.…

We introduce an optimal and nearly parameter-free algorithm for minimizing piecewise smooth (PWS) convex functions under the quadratic growth (QG) condition, where the locations and structure of the smooth regions are entirely…

Decentralized optimization over directed graphs is essential for applications such as robotic swarms, sensor networks, and distributed learning. In many practical scenarios, the underlying network takes the form of a Time-Varying Broadcast…

We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element…

This paper characterizes the well-posedness of Karush-Kuhn-Tucker system for perturbed composite optimization. Using the parabolic regularity, we introduce a novel second-order variational function, shown to be the pivotal object governing…

The problem of stopping stochastic gradient descent (SGD) in an online manner, based solely on the observed trajectory, is a challenging theoretical problem with significant consequences for applications. While SGD is routinely monitored as…

A general and new stochastic linear quadratic optimal control problem is studied, where the coefficients are allowed to be time-varying, and both state delay and control delay can appear simultaneously in the state equation and the cost…

Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance…

In this paper we study the relationship between the set of all non-negative multivariate homogeneous polynomials and those, which we call hyperwrons, whose non-negativity can be deduced from an identity involving the Wronskians of…

A topology optimization problem in a phase field setting is considered to obtain rigid structures, which are resilient to external forces and constructable with additive manufacturing. Hence, large deformations of overhangs due to gravity…

We establish a general framework that guarantees the preservation of optimal control patterns as the time horizon $[0,T]$ increases and becomes unbounded. A concept of pattern-preserving family of optimal control problems is introduced and…

We study decision-making problems where data comprises points from a collection of binary polytopes, capturing aggregate information stemming from various combinatorial selection environments. We propose a nonparametric approach for…

The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…

We present a novel framework that combines machine learning with mixed-integer optimization to solve the Capacitated Location-Routing Problem (CLRP). The CLRP is a classical NP-hard problem that integrates strategic facility location with…

Many multi-agent systems evolve by repeatedly updating each state to a weighted average of its neighbors, a process known as averaging dynamics, whose behavior becomes difficult to analyze when the interaction network varies over time. In…

We study the local convergence rate of stochastic first-order methods under a local $\alpha$-Polyak-Lojasiewicz ($\alpha$-PL) condition in a neighborhood of a target connected component $\mathcal{M}$ of the local minimizer set. The…