polyhedral approximations

Inner Approximations of Completely Positive Reformulations of Mixed Binary Quadratic Programs: A Unified Analysis

  • E. Alper Yildirim
    • Categories Global Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

    Every quadratic programming problem with a mix of continuous and binary variables can be equivalently reformulated as a completely positive optimization problem, i.e., a linear optimization problem over the convex but computationally intractable cone of completely positive matrices. In this paper, we focus on general inner approximations of the cone of completely positive matrices on … Read more

    Analysis of Copositive Optimization Based Linear Programming Bounds on Standard Quadratic Optimization

  • Gizem Sagol
  • E. Alper Yildirim
    • Categories Linear, Cone and Semidefinite Programming, Quadratic Programming Tags , , ,

    The problem of minimizing a quadratic form over the unit simplex, referred to as a standard quadratic optimization problem, admits an exact reformulation as a linear optimization problem over the convex cone of completely positive matrices. This computationally intractable cone can be approximated from the inside and from the outside by two sequences of nested … Read more