最优化与控制
We consider the Nesterov accelerated primal-dual dynamical system \[ \begin{cases} \ddot{x}(t)+\dfrac{\alpha}{t}\dot{x}(t) +\nabla f(x(t)) +A^\top\bigl(\lambda(t)+\theta t\dot{\lambda}(t)\bigr)+\beta A^\top(Ax(t)-b)=0,\\[0.6em]…
Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we…
A number of goods are called identical if they provide the same level of utility to each agent. In various real-world instances of fair division scenarios, identical indivisible items are allocated to consumers and demandants with different…
In computational science workflows, it is often the case that 1) objective functions for optimization involve multiple simulation outputs, and 2) those simulations can be performed (at least partially) in parallel. In this work, we…
Electric vehicle (EV) adoption in cold regions is hindered by degraded EV charging performance at low temperatures, which necessitates effective battery thermal management during charging. Given the coupling of battery charging and heating…
We develop the theory of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces with common noise modeled by an infinite-dimensional Wiener process that affects the dynamics of all agents. In the presence of common noise, the…
Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…
Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…
In this paper, we propose Adjusted Shuffling SARAH, a novel algorithm that integrates shuffling strategies into the recursive SARAH framework using a dynamic weighting mechanism to enhance exploration. We analyze the algorithm under two…
Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…
This paper deals with the numerical computation of the least singular value of a rectangular matrix $A$ relative to a pair of closed convex cones $(P,Q)$, which is defined as the optimal value of the non-convex optimization problem of…
In this paper, we solve the chance-constrained covariance steering problem for discrete-time Markov Jump Linear Systems (MJLS) using a convex optimization framework. We derive the analytical expressions for the mean and covariance…
The fracturing-flooding technology is a new process for the development of low-permeability oil reservoirs, achieving a series of successful applications in oilfield production. However, existing numerical simulation methods for pressure…
The goal of optimal transport (OT) is to find optimal assignments or matchings between data sets which minimize the total cost for a given cost function. However, sometimes the cost function is unknown but we have access to (parts of) the…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
We introduce Multi-Iteration Stochastic Optimizers, a novel class of first-order stochastic methods that control the relative $L^2$ error using successive control variates along the iteration path. By exploiting correlations between…
In many operational contexts, solutions to NP-hard combinatorial optimization problems, modeled by means of Mixed-Integer Linear Programming (MILP), may become infeasible due to unpredictable disruptions. Typically, reoptimizing by solving…
We consider the problem of determining feasible systems from a finite set of simulated alternatives with respect to probability constraints, where the observations from stochastic simulations are Bernoulli distributed. Most statistically…
Quadratically regularized optimal transport (QOT) is an alternative to entropic regularization that yields sparse couplings and avoids numerical instabilities due to exponential scaling. From an optimization viewpoint, the dual QOT…
Composite optimization problems, formulated as the minimization of three functions, are ubiquitous in large-scale machine learning and signal processing. While state-of-the-art splitting methods such as Condat-V\~{u} (CV) [Condat, 2013,…