mixed-integer quadratic optimization

On Tractable Convex Relaxations of Standard Quadratic Optimization Problems under Sparsity Constraints

  • Immanuel M. Bomze
  • Bo Peng
  • Yuzhou Qiu
  • E. Alper Yildirim
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming, Semi-definite Programming Tags , , , ,

    Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex relaxations of sparse StQPs arising from a mixed-binary quadratic formulation, namely, the linear optimization relaxation given by the reformulation-linearization technique, … Read more

    Mixed-Integer Quadratic Optimization and Iterative Clustering Techniques for Semi-Supervised Support Vector Machines

  • Martin Schmidt
  • Jan Pablo Burgard
  • Maria Eduarda Pinheiro
    • Categories (Mixed) Integer Nonlinear Programming, Data Science Algorithms, Data Science Applications Tags , , ,

    Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a subset of points. Furthermore, this subset can be non-representative, e.g., due to self-selection in a survey. Semi-supervised SVMs tackle … Read more

    2×2-convexifications for convex quadratic optimization with indicator variables

  • Shaoning Han
  • Andrés Gómez
  • Alper Atamturk
    • Categories (Mixed) Integer Nonlinear Programming, Semi-definite Programming Tags , , , ,

    In this paper, we study the convex quadratic optimization problem with indicator variables. For the bivariate case, we describe the convex hull of the epigraph in the original space of variables, and also give a conic quadratic extended formulation. Then, using the convex hull description for the bivariate case as a building block, we derive … Read more

    Sparse and Smooth Signal Estimation: Convexification of L0 Formulations

  • Alper Atamturk
  • Andrés Gómez
  • Shaoning Han
    • Categories (Mixed) Integer Nonlinear Programming Tags , , , ,

    Signal estimation problems with smoothness and sparsity priors can be naturally modeled as quadratic optimization with L0-“norm” constraints. Since such problems are non-convex and hard-to-solve, the standard approach is, instead, to tackle their convex surrogates based on L1-norm relaxations. In this paper, we propose new iterative conic quadratic relaxations that exploit not only the L0-“norm” … Read more