Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Các phương pháp phân tán đạo hàm bậc hai với trung bình và ứng dụng vào tối ưu hóa lưới điện
Tóm tắt
Chúng tôi nghiên cứu hiệu suất thời gian hữu hạn của một phương pháp phân tán đạo hàm bậc hai mới đây được đề xuất (DDSG) cho các bài toán tối ưu đa tác giả có ràng buộc lồi. Thuật toán này có đảm bảo về hiệu suất đối với điểm giải tối ưu cuối cùng, trái ngược với những kết quả được rút ra cho trung bình ergodic cho các thuật toán DDSG tiêu chuẩn. Công trình của chúng tôi cải thiện tốc độ hội tụ mới đây được công bố với kiểu suy giảm tỉ lệ bước cho $${{\mathcal {O}}}(\log T/\sqrt{T})$$ thành $${{\mathcal {O}}}(1/\sqrt{T})$$ với bước cố định trên một đại lượng kết hợp giữa độ không tối ưu và vi phạm ràng buộc. Sau đó, chúng tôi đánh giá số học thuật toán trên ba bài toán tối ưu hóa lưới điện. Cụ thể, đây là lập lịch đường dây trong các hệ thống điện nhiều khu vực, điều phối các nguồn năng lượng phân tán trong mạng lưới phân phối có dạng hình tia, và phân phối chung của tài sản truyền tải và phân phối. Thuật toán DDSG được áp dụng cho từng bài toán với nhiều sự thư giãn và tuyến tính hóa các phương trình dòng điện. Các thí nghiệm số học minh họa các thuộc tính khác nhau của thuật toán DDSG – so sánh với DDSG tiêu chuẩn, tác động của số lượng tác giả, và lý do tại sao gia tốc kiểu Nesterov có thể thất bại trong các cài đặt DDSG.
Từ khóa
#tối ưu hóa đa tác giả #phương pháp phân tán #đạo hàm bậc hai #ràng buộc lồi #tối ưu hóa lưới điện #nghiệm số học #mô hình hóa năng lượngTài liệu tham khảo
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