Yongchun Li

On the Partial Convexification of the Low-Rank Spectral Optimization: Rank Bounds and Algorithms

  • Yongchun Li
  • Weijun Xie
    • Categories Integer Programming Tags , , , ,

    A Low-rank Spectral Optimization Problem (LSOP) minimizes a linear objective subject to multiple two-sided linear matrix inequalities intersected with a low-rank and spectral constrained domain set. Although solving LSOP is, in general, NP-hard, its partial convexification (i.e., replacing the domain set by its convex hull) termed “LSOP-R”, is often tractable and yields a high-quality solution. … Read more

    On the Exactness of Dantzig-Wolfe Relaxation for Rank Constrained Optimization Problems

  • Yongchun Li
  • Weijun Xie
    • Categories Integer Programming Tags , , , , , ,

    In the rank-constrained optimization problem (RCOP), it minimizes a linear objective function over a prespecified closed rank-constrained domain set and $m$ generic two-sided linear matrix inequalities. Motivated by the Dantzig-Wolfe (DW) decomposition, a popular approach of solving many nonconvex optimization problems, we investigate the strength of DW relaxation (DWR) of the RCOP, which admits the … Read more

    D-optimal Data Fusion: Exact and Approximation Algorithms

  • Yongchun Li
  • Marcia Fampa
  • Jon Lee
  • Feng Qiu
  • Weijun Xie
    • Categories Combinatorial Optimization, Integer Programming Tags , , , , , , ,

    We study the D-optimal Data Fusion (DDF) problem, which aims to select new data points, given an existing Fisher information matrix, so as to maximize the logarithm of the determinant of the overall Fisher information matrix. We show that the DDF problem is NP-hard and has no constant-factor polynomial-time approximation algorithm unless P = NP. … Read more

    Beyond Symmetry: Best Submatrix Selection for the Sparse Truncated SVD

  • Yongchun Li
  • Weijun Xie
    • Categories Combinatorial Optimization, Data-Mining, Integer Programming Tags , , , ,

    Truncated singular value decomposition (SVD), also known as the best low-rank matrix approximation, has been successfully applied to many domains such as biology, healthcare, and others, where high-dimensional datasets are prevalent. To enhance the interpretability of the truncated SVD, sparse SVD (SSVD) is introduced to select a few rows and columns of the original matrix … Read more

    Exact and Approximation Algorithms for Sparse PCA

  • Yongchun Li
  • Weijun Xie
    • Categories Integer Programming Tags , , , , ,

    Sparse PCA (SPCA) is a fundamental model in machine learning and data analytics, which has witnessed a variety of application areas such as finance, manufacturing, biology, healthcare. To select a prespecified-size principal submatrix from a covariance matrix to maximize its largest eigenvalue for the better interpretability purpose, SPCA advances the conventional PCA with both feature … Read more

    Best Principal Submatrix Selection for the Maximum Entropy Sampling Problem: Scalable Algorithms and Performance Guarantees

  • Yongchun Li
  • Weijun Xie
    • Categories Data-Mining

    This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix with a given size out of a covariance matrix from a system. MESP has been widely applied to many areas, including healthcare, power system, manufacturing, data science, etc. Investigating its Lagrangian dual and primal characterization, we … Read more