最优化与控制

This article discusses an optimal control problem for a phase field model of two immiscible incompressible fluid flow, incorporating surface tension effects. The optimal control problem is defined with a $L^2$-cost functional and subject to…

Global polynomial optimization methods typically rely on compactness of the feasible region in order to find solutions. These methods can incur considerable computational expense and most commercially available solvers do not verify the…

In this paper, we establish the existence of solutions for a particular class of degenerate hyperbolic equations. Following this, we approximate these degenerate equations by employing a sequence of uniformly hyperbolic equations. Notably,…

This paper presents an H2-optimal model order reduction (MOR) method for linear systems with quadratic outputs based on Riemannian optimization. The H2-optimal MOR is formulated as an optimization problem in which the optimization variables…

We propose a generative framework for learning stochastic dynamics from endpoint and intermediate distributional observations. The method formulates generation as a McKean-Vlasov control problem in which terminal and time-marginal laws are…

This paper presents a computationally efficient approach for Gaussian process model predictive control (GP-MPC), where Gaussian process (GP) regression is used to complement a baseline model of the system dynamics. The proposed method…

Large-scale machine learning models are trained on clusters of machines that exhibit heterogeneous performance due to hardware variability, network delays, and system-level instabilities. In such environments, time complexity rather than…

We design Local LMO - a new projection-free gradient-type method for constrained optimization. The key algorithmic idea is to replace the global linear minimization oracle over the constraint set used by Frank-Wolfe (FW) with a local linear…

In this paper, we propose several set-point control schemes for achieving finite-time regulation in a class of Euler--Lagrange systems with $n$ degrees of freedom and uncertain potential energy. The proposed controllers are based on…

Simple cardinality refers to counting nonzero elements of an independent variable satisfying certain properties. Composite cardinality is a simple counting process composited with an affine mapping, and is therefore more complicated than…

Davydov, Moldavskaya, and Zitikis introduced local indices for quantifying the lack of convexity of a \(C^2\) function by measuring the nuclear-norm distance of its Hessian from the cone of positive semidefinite matrices. This paper…

We develop a unified Lyapunov-integral quadratic constraint (IQC) framework for establishing uniform stability of first-order accelerated optimization algorithms in the $\beta$-smooth and $\gamma$-strongly convex regime. Classical analyses…

Robust learning aims to maintain model performance under noise, corruption, and distributional shifts, which are prevalent in modern machine learning applications. This work shows that examples of robust learning problems can be formulated…

Self-optimizing control (SOC) aims to maintain near-optimal process operation by judiciously selecting controlled variables (CVs). In this series of work, the generalized global SOC (g2SOC) approach is proposed, which extends the concept of…

Solving optimal control problems via large-scale NLP solvers depends on discretizing continuous dynamics. Yet, this transcription step hides critical vulnerabilities-most notably truncation error and invariant drift-that can drive solvers…

In this framework, the extremal case corresponds to the tightest nontrivial relaxation in this hierarchy, in which every proper principal submatrix is constrained to be positive semidefinite, while the global positive semidefiniteness…

We study the optimal design of stealthy attacks against partially observed linear control systems. We first propose a novel likelihood-based detection mechanism derived from the innovation process, based on which we quantify stealthiness…

We investigate the Stochastic Krasnoselskii-Mann iterations for expected nonexpansive fixed-point problems in a real Hilbert space. We establish convergence guarantees under significantly weaker assumptions on the variance than those…

The Method of Ellipcenters (ME), introduced in~\cite{ME2025} for strongly convex quadratic minimization, uses two gradient evaluations per iteration: one at the current iterate and one at a companion point on the same level set. We extend…

This paper proposes a novel mathematical framework for modeling uncertainties in supOU processes, a common model for long-memory phenomena. We address uncertainties as distortions in reversion and Levy measures, evaluating them…