partition

A Fully Distributed Dual Consensus ADMM Based on Partition for DC-OPF with Carbon Emission Trading

  • Zhaoyang Dong
  • Jiangyao Luo
  • Yan Xu
  • Linfeng Yang
  • Zhenrong Zhang
    • Categories Applications - Science and Engineering, Energy Tags , , , ,

    This paper presents a novel fully distributed alternating direction method of multipliers (ADMM) approach for solving the direct current optimal power flow with carbon emission trading (DC-OPF-CET) problem. Different from the other ADMM-based distributed approaches which disclosing boundary buses and branches information among adjacent subsystems, our proposed method adopts a new strategy by using ADMM … Read more

    Partition of a Set of Integers into Subsets with Prescribed Sums

  • Wang Yiju
    • Categories Graphs and Matroids Tags , ,

    A nonincreasing sequence of positive integers $\langle m_1,m_2,\cdots,m_k \rangle$ is said to be {\em $n$-realizable\/} if the set $I_n=\{ 1,2,\cdots,n\}$ can be partitioned into $k$ mutually disjoint subsets $S_1,S_2,\cdots, S_k$ such that $\sum\limits_{x\in S_i}x=m_i$ for each $1\le i\le k$. In this paper, we will prove that a nonincreasing sequence of positive integers $\langle m_1,m_2,\cdots,m_k\rangle$ is … Read more

    Sparsity issues in the computation of Jacobian Matrices

  • Shahadat Hossain
  • Trond Steihaug
    • Categories Nonlinear Optimization Tags , , ,

    The knowledge of sparsity information plays an important role in efficient determination of sparse Jacobian matrices. In a recent work, we have proposed sparsity-exploiting substitution techniques to determine Jacobian matrices. In this paper, we take a closer look at the underlying combinatorial problem. We propose a column ordering heuristic to augment the “usable sparsity” in … Read more

    Reducing the number of AD passes for computing a sparse Jacobian matrix

  • Shahadat Hossain
  • Trond Steihaug
    • Categories Graphs and Matroids, Nonlinear Systems and Least-Squares Tags , ,

    A reduction in the computational work is possible if we do not require that the nonzeros of a Jacobian matrix be determined directly. If a column or row partition is available, the proposed substitution technique can be used to reduce the number of groups in the partition further. In this chapter, we present a substitution … Read more