最优化与控制

We present an optimal control problem to guide the selection of morphology classes arising in organic solar cells. The study focuses on phase separation processes in polymer solvent mixtures, with particular attention to solvent evaporation…

This tutorial provides an overview of the generalized Lyapunov method (GLM) for analyzing input-to-state stability (ISS) of partial differential equations (PDEs). We begin by revisiting the classical Lyapunov method and the standard…

In this paper, we propose a single-loop stochastic gradient algorithm for solving stochastic nonconvex-concave minimax optimization with nonlinear convex coupled constraints (MCC). The proposed method, SPACO (Stochastic Penalty-based…

We investigate a hierarchical control problem for a one-dimensional Stefan system with localized distributed controls. The setting combines a Stackelberg strategy with a Nash equilibrium among multiple followers, yielding a multi-objective…

We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is…

This paper studies a variant of the Set Covering Routing Problem (SCRP) motivated by post-disaster humanitarian logistics. We consider a hybrid distribution concept in which the majority of transportation is performed by helicopters, while…

We consider smooth convex minimization over compact convex sets, i.e., $\min_{x \in C} f(x)$ with the (vanilla) Frank-Wolfe algorithm. Well-known lower bounds establish a worst-case $\Omega(1/t)$ primal-gap barrier in the general smooth…

We study a distributed optimal control problem for a nonisothermal Caginalp-type phase-field model that describes tumour growth under thermal therapy. The PDE system couples a possibly viscous Cahn-Hilliard equation, governing the evolution…

This paper presents a unified string-stability framework for leader-follower multi-agent systems governed by first-, second-, and m-th order consensus protocols operating under an r-predecessor directed communication topology. While string…

In this work, we develop a control-theoretic framework for constrained optimization problems with composite objective functions including non-differentiable terms. Building on the proximal augmented Lagrangian formulation, we construct a…

In this work, we first prove that the separation principle holds for communication-constrained LQR problems under i.i.d. zero-mean disturbances with a symmetric distribution. We then solve the dynamic programming problem and show that the…

In this article, we establish exponential turnpike theorems for a class of nonlinear deterministic meanfield optimal control problems. We carry out our analysis simultaneously in the so-called Lagrangian and Eulerian frameworks. In the…

Optimization algorithms are unlikely to converge to strict saddle points. Proofs to that effect rely on the Center-Stable Manifold Theorem (CSMT), casting algorithms as dynamical systems: $x_{k+1} = g_k(x_k)$. In its standard form, the CSMT…

Concerning huge-scale aggregative convex programming of a linear objective subject to the affine constraints of equality and inequality and the quadratic constraints of inequality, convex and aggregatively computable, an algorithm is…

This paper analyzes and explicitly solves a class of long-term average impulse control problems and a related class of singular control problems. The underlying process is a general one-dimensional diffusion with appropriate boundary…

The notion of regular pair $(A,B)$ for two nonempty closed convex subsets $A$ and~$B$ of a Hilbert space $\H$ was introduced by Borwein and Bauschke in 1993 to ensure convergence (in norm) of the alternating projection method to some point…

Designing effective score functions in Conformal Prediction (CP) for time-series data remains challenging due to conservativeness and/or computational inefficiency. We propose Optimal Selection Conformal Prediction (OSCP), which…

Nonconvex and nonsmooth bi-level optimization poses critical theoretical challenges, while arising in several applications. In this work, we develop a method for nonconvex, nonsmooth bi-level optimization and introduce Binno, a first-order…

We address in this paper a fundamental question that arises in mean-field games (MFGs), namely whether mean-field equilibria (MFE) for discrete-time finite-horizon MFGs can be used to obtain approximate stationary as well as non-stationary…

When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…