Convex Relaxation Methods for Community Detection

islanding detection methods for microgrids

امروزه استفاده از منابع انرژی پراکنده کاربرد وسیعی یافته است . اگر چه این منابع بسیاری از مشکلات شبکه را حل می کنند اما زیاد شدن آنها مسائل فراوانی برای سیستم قدرت به همراه دارد . استفاده از میکروشبکه راه حلی است که علاوه بر استفاده از مزایای منابع انرژی پراکنده برخی از مشکلات ایجاد شده توسط آنها را نیز منتفی می کند . همچنین میکروشبکه ها کیفیت برق و قابلیت اطمینان تامین انرژی مشترکان را افزایش ...

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Complexity Analysis of Successive Convex Relaxation Methods for Nonconvex Sets

This paper discusses computational complexity of conceptual successive convex relaxation methods proposed by Kojima and Tunn cel for approximating a convex relaxation of a compact subset F = fx 2 C 0 : p(x) 0 (8p() 2 P F)g of the n-dimensional Euclidean space R n. Here C 0 denotes a nonempty compact convex subset of R n , and P F a set of nitely or innnitely many quadratic functions. We evaluat...

Community Detection via Semidefinite Relaxation

Notes for lecture given by the author on November 7, 2014 as part of the special course: “Randomness, Matrices and High Dimensional Problems”, at IMPA, Rio de Janeiro, Brazil. The results presented in these notes are from [1]. 1. The problem we will focus on Let n be an even positive integer. Given two sets of n2 nodes consider the following random graph G: For each pair (i, j) of nodes, (i, j)...

Distributed Asynchronous Relaxation Methods for Convex Network Flow Problems

We consider the solution of the single commodity strictly convex network flow problem in a distributed asynchronous computation environment. The dual of this problem is unconstrained, differentiable, and well suited for solution via Gauss-Seidel relaxation. We show that the structure of the dual allows the successful application of a distributed asynchronous method whereby relaxation iterations...