A Row-Stochastic Event-Based Quantized Algorithm for Distributed Optimization With Linear Convergence.

Area of Science:

• Distributed Optimization
• Control Systems
• Networked Systems

Background:

• Distributed optimization faces challenges from communication constraints like limited cost and bandwidth.
• Existing algorithms often struggle with the negative impacts of these communication limitations.
• Need for robust algorithms that can maintain performance under restricted communication.

Purpose of the Study:

• To propose a new algorithm, row-stochastic event-based quantized (RSEQ), for distributed optimization.
• To address communication constraints by designing a novel event-based dynamic quantizer.
• To achieve linear convergence to the global optimal solution efficiently.

Main Methods:

• Developed a row-stochastic event-based dynamic quantizer with an event generator and dynamic encoder/decoder.
• Introduced an acceleration term for linear convergence without an average gradient estimator.
• Employed a Perron vector estimator to manage directed network unbalancedness, which can become inactive.

Main Results:

• The RSEQ algorithm demonstrates lower conservatism compared to column-stochastic matrix-based methods.
• Achieved linear convergence to the global optimal solution.
• Showcased effective performance in a smart grid economic dispatch problem.

Conclusions:

• RSEQ effectively handles communication constraints in distributed optimization.
• The algorithm enables linear convergence even with directed networks and limited communication.
• Event-based quantization and Perron vector estimation are key to RSEQ's success.