299 papers
This paper proposes HSM-ADMM, a novel distributed stochastic algorithm for nonconvex composite optimization that achieves optimal complexity with a single-loop structure and minimal communication by employing node-specific adaptive step sizes to decouple convergence stability from global network properties.
This paper establishes the existence, uniqueness, and sharp boundary asymptotics of large solutions to semilinear elliptic equations with gradient-dependent terms and singular weights, while also proving their strict convexity and identifying them as value functions for infinite-horizon stochastic optimal control problems.
This paper establishes the open-loop solvability and derives a closed-loop representation for a cone-constrained two-player zero-sum stochastic linear-quadratic differential game involving jump-diffusion systems with regime switching and random coefficients, utilizing forward-backward stochastic differential equations and newly proposed multidimensional indefinite extended stochastic Riccati equations with jumps.
This paper proposes a model-free predictive tracking algorithm for unknown nonlinear systems with Koopman linear embeddings that leverages Willems' fundamental lemma to achieve dynamic regret decaying exponentially with the prediction horizon, effectively bridging the performance gap between nonlinear and lifted linear counterparts.
This paper establishes sufficient conditions for the existence of longest arcs in left-invariant three-dimensional contact sub-Lorentzian structures on solvable Lie groups and the universal cover of SL(2, R), addressing the nontrivial existence question inherent in such optimal control problems with unbounded control sets.
This paper investigates a one-parametric family of left-invariant, SO(1,1)-symmetric Lorentzian structures on the universal covering of SL(2,R), analyzing their global geodesic optimality and examining how these properties deform into those of a limiting sub-Lorentzian structure.
This paper proposes a novel bidding algorithm for repeated contextual first-price auctions with budget constraints under one-sided information feedback, utilizing a robust regression method based on conditional quantile invariance to learn unknown competitor bid distributions and achieving order-optimal regret.
The paper introduces the Inexact Bregman Sparse Newton (IBSN) method, a novel algorithm that combines a Bregman proximal point framework with a sparse Newton solver and Hessian sparsification to efficiently compute exact Optimal Transport distances for large-scale datasets while guaranteeing global convergence and outperforming existing state-of-the-art methods in both speed and precision.
This paper presents a detailed implementation of Riemannian Newton's method for optimization on the indefinite Stiefel manifold by deriving the Levi-Civita connection and analytically computing the Hessian under two existing metrics, then solving the resulting Newton equation in the tangent space via the linear conjugate gradient method to achieve fast local convergence.
This paper introduces a novel high-resolution ODE framework based on -resolution analysis to overcome the limitations of existing methods in studying first-order algorithms with momentum, providing deeper insights into their convergence properties and enabling provably optimal modifications for methods like PDHG and Heavy-Ball.
This paper extends the geometric simplex method to linear programs in locally convex topological vector spaces by replacing algebraic pivoting with a generalized geometric framework, thereby establishing convergence conditions and proving that all such polytopes possess exposed extreme points connected by edge paths, including complex cases like the Hilbert cube.
This paper resolves an open question in convex optimization by proving that the gradient-evaluation sequence in Nesterov's accelerated gradient descent method, including in projection-based and non-Euclidean settings, achieves the optimal convergence rate for the objective function value, matching the performance of the standard solution sequence.
This paper introduces a Gauss-Newton method for large-scale PDE-constrained inverse problems, such as Full-Waveform Inversion, that achieves fast convergence without requiring additional PDE solves beyond those needed for gradient evaluation.
This paper presents a two-stage stochastic optimization framework, implemented in the open-source tool *OptBio*, to guide risk-adjusted investment and operational planning for diversified sugarcane-based biofuel and bioelectricity facilities under market uncertainty, demonstrating through a Brazilian case study that risk-averse strategies favor diversification while highlighting the potential viability of biomethane, hydrogen, and biochar.
This paper presents small-scale prototype testing and a novel, computationally-efficient control allocation algorithm for the CABLESSail concept, demonstrating its ability to effectively manage solar sail momentum through cable-actuated shape control while maintaining robustness against membrane shape uncertainties.
This paper evaluates the capabilities of various large language models, including Llama-3 and ChatGPT, in solving diverse discrete optimization problems using natural language datasets, revealing that while stronger models generally perform better, Chain-of-Thought reasoning is not universally effective and data augmentation can improve performance on simpler tasks despite introducing instability.
This paper proposes the F²SA- method, which utilizes -th order finite differences to achieve a nearly optimal complexity for finding -stationary points in stochastic bilevel optimization with highly smooth objectives, thereby improving upon previous first-order bounds and matching the fundamental lower limit.
This paper establishes a maximum principle and the Hamilton-Jacobi-Bellman equation for optimal control on infinite-dimensional probability distribution spaces, and leverages these theoretical results to develop a scalable deep learning algorithm for solving high-dimensional multi-agent control problems.
This paper establishes that policy gradient methods achieve global convergence with non-asymptotic sample complexity guarantees for finite-horizon MDPs with general state and action spaces by proving the Polyak-Łojasiewicz-Kurdyka condition holds, thereby providing the first theoretical foundations for optimizing multi-period inventory and stochastic cash balance systems.
This paper investigates how malicious auditees can construct fairness-compliant yet representative-looking samples from non-compliant distributions to deceive auditors, formalizes these manipulation strategies using optimal transport and entropic projections, and proposes statistical tests to detect such distributional manipulation attacks.