Matrix-valued distributed stochastic optimization with constraints

2023, Volume 24, Issue 9

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Frontiers of Information Technology & Electronic Engineering >> 2023, Volume 24, Issue 9 doi: 10.1631/FITEE.2200381

Matrix-valued distributed stochastic optimization with constraints

1.Key Laboratory of Intelligent Education Technology and Application of Zhejiang Province, Zhejiang Normal University, Jinhua 321004, China ;; 2.School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China ;; 3.School of Mathematical Sciences, Fudan University, Shanghai 200433, China ;; 4.School of Automation, Central South University, Changsha 410083, China

Received: 2022-09-07 Accepted: 2023-09-21 Available online: 2023-09-21

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Abstract

In this paper, we address matrix-valued distributed stochastic optimization with inequality and equality constraints, where the objective function is a sum of multiple matrix-valued functions with stochastic variables and the considered problems are solved in a distributed manner. A penalty method is derived to deal with the constraints, and a selection principle is proposed for choosing feasible penalty functions and penalty gains. A distributed optimization algorithm based on the gossip model is developed for solving the stochastic optimization problem, and its convergence to the optimal solution is analyzed rigorously. Two numerical examples are given to demonstrate the viability of the main results.

Keywords

Distributed optimization ; Matrix-valued optimization ; Stochastic optimization ; Penalty method ; Gossip model

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