最优化与控制
A phylogenetic tree is an edge-weighted binary tree, with leaves labelled by a collection of species, that represents the evolutionary relationships between those species. For such a tree, a phylogenetic diversity index is a function that…
In this paper we develop a Stochastic Gradient Langevin Dynamics (SGLD) algorithm tailored for solving a certain class of non-convex distributionally robust optimisation (DRO) problems. By deriving non-asymptotic convergence bounds, we…
To address efficiency and design challenges in choice-based matching platforms, we introduce a two-sided assortment optimization framework under general choice preferences. The goal in this problem is to maximize the expected number of…
We study two variants of the mirror descent-ascent (MDA) algorithm for solving min-max problems on the space of measures: simultaneous and alternating. We work under assumptions of convexity-concavity and relative smoothness of the payoff…
In this paper, we introduce a deterministic formulation for the geometric programming problem, wherein the coefficients are represented as independent linear-normal uncertain random variables. To address the challenges posed by this…
We study a McKean-Vlasov Forward-Backward Stochastic Differential Equation (FBSDE) in connection with the theory of Stochastic Differential Mean-Field games, particularly the weak (non-fully coupled) formulation described in Section 3.3.1…
The NEPv approach has been increasingly used lately for optimization on the Stiefel manifold arising from machine learning. General speaking, the approach first turns the first order optimality condition, also known as the KKT condition,…
This study presents a novel deterministic optimization algorithm based on a special variant of the Linear Congruential Generator (LCG). While conventional algorithms generally operate within the search space, the introduced technique…
This paper explores the controllability of a class of N-dimensional hyperbolic equations featuring a single interior degenerate point. Firstly, we establish the well-posedness of the equation through the application of the Hardy inequality.…
We present CHAP (Coordinating Heuristics Across Platforms) a GPU-CPU-hybrid primal heuristic framework for mixed-integer programming. CHAP adopts a portfolio approach where it coordinates a set of primal heuristics, including Local Search,…
This work explores the global optimization problem of finding lowest-energy configurations (ground states) in disordered continuous spins models from statistical physics, with a particular focus on the random field XY model. Due to an…
We study the computational complexity of decision problems in $k$-level linear programming (LP). Seminal work by Jeroslow establishes that determining whether the optimal objective value of a $k$-level LP is at least as good as a given…
Recent LLM-driven discoveries have renewed interest in geometric packing problems. In this paper, we study several classes of such packing problems through the lens of modern global nonlinear optimization. Starting from comparatively direct…
Parameter identification is crucial in virtual engineering processes, yet determining appropriate system excitations for identifying specific parameters remains challenging. In practice, extensive experimental programs often fail to…
Energy system optimization models are increasing in scope and resolution, yielding large and challenging linear programs. For a long time, the standard way to address such problems has relied on shared-memory interior-point methods (IPM),…
We study stochastic optimization from a joint continuous-discrete point of view. Starting from a second-order stochastic differential equation interpreted as a noisy accelerated gradient flow, we discretize the dynamics by a fully implicit…
This study investigates real-time assignment decisions for extraboard transit operators, who are responsible for covering open work due to unexpected events such as driver absenteeism. Efficient usage of extraboard operators is critical as…
We study the policy evaluation problem in multi-agent reinforcement learning (MARL) over directed communication networks, where agents cooperate with each other to explore an unknown environment and accomplish a specific task. We propose a…
We develop an adaptive feedback control technique that combines an extremum-seeking-based command generator (ECG) with indirect adaptive control. In particular, ECG is used to generate commands that asymptotically optimize a cost function…
This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional in an infinite horizon. A main difficult is well-posedness of the BSDE in $L^1$ and in infinite horizon. A notion of…