Jieqiu Chen

A First-Order Smoothing Technique for a Class of Large-Scale Linear Programs

  • Samuel Burer
  • Jieqiu Chen
    • Categories Data-Mining, Linear Programming, Nonsmooth Optimization Tags , , ,

    We study a class of linear programming (LP) problems motivated by large-scale machine learning applications. After reformulating the LP as a convex nonsmooth problem, we apply Nesterov’s primal-dual smoothing technique. It turns out that the iteration complexity of the smoothing technique depends on a parameter $\th$ that arises because we need to bound the originally … Read more

    Globally Solving Nonconvex Quadratic Programming Problems via Completely Positive Programming

  • Samuel Burer
  • Jieqiu Chen
    • Categories Global Optimization, Optimization Software and Modeling Systems, Quadratic Programming Tags , , , ,

    Nonconvex quadratic programming (QP) is an NP-hard problem that optimizes a general quadratic function over linear constraints. This paper introduces a new global optimization algorithm for this problem, which combines two ideas from the literature—finite branching based on the first-order KKT conditions and polyhedral-semidefinite relaxations of completely positive (or copositive) programs. Through a series of … Read more