A gradient‐free distributed optimization method for convex sum of nonconvex cost functions

Pang, Yipeng; Hu, Guoqiang

doi:10.1002/rnc.6266

Cited by 4 publications

(1 citation statement)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also refer to the papers 9,10,16,36,41 regrading the delay issue in the communication. We also refer to the distributed optimization problem on directed graphs 24,45 , the gradient-free distributed optimization algorithms 28,40 , and the fixed time optimization problems 19 .…”

Section: Introductionmentioning

confidence: 99%

Convergence property of the Quantized Decentralized Gradient descent with constant stepsizes and an effective strategy for the stepsize selection

Lee

Choi

2023

Preprint

View full text Add to dashboard Cite

Distributed algorithms involving quantization have received a lot of interest recently as the quantized communication appears naturally in real applications. For such algorithms, it is non-trivial to select appropriate stepsizes for high performance, due to presence of the noise effect induced from quantization. In this paper, we establish new convergence results for the quantized decentralized gradient descent and we propose a novel strategy of choosing the stepsizes for the high performance of the algorithm. Precisely, under the strongly convexity assumption on the aggregate cost function and the smoothness assumption on each local cost function, we prove the algorithm converges exponentially fast to a small neighborhood of the optimizer whose radius depends on the stepsizes. Then, based on our convergence result, we suggest an effective stepsize selection algorithm which repeats diminishing the stepsizes after a number of specific iterations by a certain rule. Both the convergence results and the effectiveness of the suggested stepsize selection are also verified by the numerical experiments.

show abstract

Section: Introductionmentioning

confidence: 99%

Convergence property of the Quantized Decentralized Gradient descent with constant stepsizes and an effective strategy for the stepsize selection

Lee

Choi

2023

Preprint

View full text Add to dashboard Cite

show abstract

A gradient‐free distributed optimization method for convex sum of nonconvex cost functions

Pang

2022

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

This article presents a special type of distributed optimization problems, where the summation of agents' local cost functions (i.e., global cost function) is convex, but each individual can be nonconvex. Unlike most distributed optimization algorithms by taking the advantages of gradient, the considered problem is allowed to be nonsmooth, and the gradient information is unknown to the agents. To solve the problem, a Gaussian‐smoothing technique is introduced and a gradient‐free method is proposed. We prove that each agent's iterate approximately converges to the optimal solution both with probability 1 and in mean, and provide an upper bound on the optimality gap, characterized by the difference between the functional value of the iterate and the optimal value. The performance of the proposed algorithm is demonstrated by a numerical example and an application in privacy enhancement.

show abstract

A Distributed Optimization Approach for Collaborative Object Lifting Using Multiple Aerial Robots

Liu,

Sun,

Feng

et al. 2024

Un. Sys.

View full text Add to dashboard Cite

In the past decade, multi-robot collaborative object transport has garnered significant attention, with the majority of research targeting transport strategies. This study recasts the collaborative object lifting challenge into an optimization problem framework. Within this setup, each robot leverages a local evaluation function to determine its lifting location. Collectively, these robots strive to optimize a unified evaluation function. An intertwined equation constraint is embedded within the optimization schema, ensuring that the system’s mass center remains stable throughout the lifting process. Furthermore, we impose local feasibility constraints, thereby delimiting the optimal lifting location to a specified region. This research introduces several algorithms, differentiated based on the constraints applied to robot velocity. By harnessing these algorithms, robots can autonomously pinpoint the most apt lifting location that aligns with predetermined criteria. This methodology necessitates a robot to engage in exchanges of auxiliary variables solely with its immediate peers. Noteworthily, parameters such as location, velocity, and mass are accessed in a localized manner, reinforcing data privacy and reducing communication burdens. The paper concludes with a robust mathematical validation that underscores asymptotic convergence to the exact optimal lifting location, underpinned by numerical simulations which attest to the potency of the proposed algorithms.

show abstract

A gradient‐free distributed optimization method for convex sum of nonconvex cost functions

Cited by 4 publications

References 47 publications

Convergence property of the Quantized Decentralized Gradient descent with constant stepsizes and an effective strategy for the stepsize selection

Convergence property of the Quantized Decentralized Gradient descent with constant stepsizes and an effective strategy for the stepsize selection

A gradient‐free distributed optimization method for convex sum of nonconvex cost functions

A Distributed Optimization Approach for Collaborative Object Lifting Using Multiple Aerial Robots

Contact Info

Product

Resources

About