最优化与控制
Neural operator (NO) architectures learn nonlinear maps between infinite-dimensional function spaces and are widely used to accelerate simulation and enable data-driven model discovery. While universality results ensure expressivity, they…
Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…
Nonsmooth composite optimization problems under uncertainty are prevalent in various scientific and engineering applications. We consider risk-neutral composite optimal control problems, where the objective function is the sum of a…
In this paper, we focus on solving the optimal control problem for integral stochastic Volterra equations in a finite dimensional setting. In our setting, the noise term is driven by a pure jump L\'evy noise and the control acts on the…
We investigate the optimal control of large-scale autonomous systems under explicitly adversarial conditions, incorporating the probabilistic destruction of agents over time. In many such systems, adversarial interactions arise as different…
Hyperbolic (HB) programming generalizes many popular convex optimization problems, including semidefinite and second-order cone programming. Despite substantial theoretical progress on HB programming, efficient computational tools for…
We study free orthotropic material optimization for two-dimensional plane-stress compliance minimization with two well-ordered isotropic phases, motivated by the gap between tensors admissible in classical free-material optimization and…
This paper addresses boundary prescribed-time stabilization of a one-dimensional heat equation with spatially and temporally varying coefficients. In contrast to asymptotic or exponential stabilization, prescribed-time stabilization ensures…
This paper studies the long-time behavior of stochastic differential inclusions driven by maximal monotone operators, motivated by continuous-time models of first-order optimization methods under noisy or approximate operator information.…
We study Frank-Wolfe (FW) methods for constrained bilevel optimization when the lower-level problem is solved only approximately, yielding biased and inexact hypergradients. We analyze inexact variants of vanilla FW as well as away-step and…
We establish a rigorous existence theory for the quantum splines introduced by Brody, Holm, and Meier in Physical Review Letters (2012). These curves arise as solutions of a variational problem on the unitary group describing optimally…
We provide a convergence result for sequences of random variables taking values in a metric space that satisfy a stochastic quasi-Fej\'er monotonicity condition, in the context of a (local) compactness assumption. Our result is quantitative…
This paper addresses a distributed nonconvex optimization problem over multi-agent networks, where each agent exchanges its local information solely with its neighbors. Given that most existing distributed nonconvex optimization algorithms…
Lifting is a crucial technique in mixed integer programming (MIP) for generating strong valid inequalities, which serve as cutting planes to improve the branch-and-cut algorithm. We first propose an exact sequential lifting algorithm for…
We consider the oracle complexity of constrained convex optimization given access to a Linear Minimization Oracle (LMO) for the constraint set and a gradient oracle for the $L$-smooth, strongly convex objective. This model includes…
Dantzig-Wolfe reformulation is a widely used technique for obtaining stronger relaxations in the context of branch-and-bound methods for solving integer optimization problems. Arc-Flow reformulations are a lesser known technique related to…
Despite its nonconvexity, policy optimization for the Linear Quadratic Regulator (LQR) admits a favorable structural property known as gradient dominance, which facilitates linear convergence of policy gradient methods to the globally…
In this paper, we study a class of bilevel optimization program (BP), where the feasible set of the lower level program is independent of the upper level variable. For bilevel programs it is known that the first order approach requires the…
Model Predictive Control (MPC) offers a versatile framework for constraint handling and multi-objective optimisation, yet practical application faces challenges regarding initial and recursive feasibility, robustness against model…
We study huge-scale assortment optimization problems to maximize expected revenue under customer choice, addressing a fundamental challenge in industries such as transportation, retail, and healthcare. The choice-based linear programming…