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The distributed subgradient method (DSG) is a widely discussed algorithm to cope with large-scale distributed optimization problems in the arising machine learning applications. Most exisiting works on DSG focus on ideal communication…

The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…

Distributed optimization increasingly plays a central role in economical and sustainable operation of cyber-physical systems. Nevertheless, the complete potential of the technology has not yet been fully exploited in practice due to…

The diffusion model has shown success in generating high-quality and diverse solutions to trajectory optimization problems. However, diffusion models with neural networks inevitably make prediction errors, which leads to constraint…

Chance-constrained programs (CCPs) constitute a difficult class of stochastic programs due to its possible nondifferentiability and nonconvexity even with simple linear random functionals. Existing approaches for solving the CCPs mainly…

This paper investigates the stochastic program with the chance constraint on a quadratic form of random variables following multivariate Gaussian mixture distribution (GMD). Under some mild conditions, it is proved that the asymptotic…

Distributed optimization utilizes local computation and communication to realize a global aim of optimizing the sum of local objective functions. This article addresses a class of constrained distributed nonconvex optimization problems…

Constrained clustering leverages limited domain knowledge to improve clustering performance and interpretability, but incorporating pairwise must-link and cannot-link constraints is an NP-hard challenge, making global optimization…

Chance constrained program is computationally intractable due to the existence of chance constraints, which are randomly disturbed and should be satisfied with a probability. This paper proposes a two-layer randomized algorithm to address…

This paper proposes a distributed dual gradient tracking algorithm (DDGT) to solve resource allocation problems over an unbalanced network, where each node in the network holds a private cost function and computes the optimal resource by…

Diffusion Language Models (DLMs) have recently achieved significant success due to their any-order generation capabilities. However, existing inference methods typically rely on local, immediate-step metrics such as confidence or entropy…

In this work, we consider solving a distributed optimization problem in a multi-agent network with multiple clusters. In each cluster, the involved agents cooperatively optimize a separable composite function with a common decision…

This paper studies a distributionally robust chance constrained program (DRCCP) with Wasserstein ambiguity set, where the uncertain constraints should be satisfied with a probability at least a given threshold for all the probability…

Implementing Decentralized Gradient Descent (DGD) in wireless systems is challenging due to noise, fading, and limited bandwidth, necessitating topology awareness, transmission scheduling, and the acquisition of channel state information…

Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…

This paper presents a novel deep learning based data-driven optimization method. A novel generative adversarial network (GAN) based data-driven distributionally robust chance constrained programming framework is proposed. GAN is applied to…

This paper presents a novel algorithm that leverages Stochastic Gradient Descent strategies in conjunction with Random Features to augment the scalability of Conic Particle Gradient Descent (CPGD) specifically tailored for solving sparse…

This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the…

Diffusion models have shown remarkable potential in planning and control tasks due to their ability to represent multimodal distributions over actions and trajectories. However, ensuring safety under constraints remains a critical challenge…

Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…