completely positive programming relaxation

Lagrangian-Conic Relaxations, Part I: A Unified Framework and Its Applications to Quadratic Optimization Problems

  • Naohiko Arima
  • Sunyoung Kim
  • Masakazu Kojima
  • Kim-Chuan Toh
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    In Part I of a series of study on Lagrangian-conic relaxations, we introduce a unified framework for conic and Lagrangian-conic relaxations of quadratic optimization problems (QOPs) and polynomial optimization problems (POPs). The framework is constructed with a linear conic optimization problem (COP) in a finite dimensional vector space endowed with an inner product, where the … Read more

    Simplified Copositive and Lagrangian Relaxations for Linearly Constrained Quadratic Optimization Problems in Continuous and Binary Variables

  • Naohiko Arima
  • Sunyoung Kim
  • Masakazu Kojima
    • Categories Linear, Cone and Semidefinite Programming Tags , , , ,

    For a quadratic optimization problem (QOP) with linear equality constraints in continuous nonnegative variables and binary variables, we propose three relaxations in simplified forms with a parameter $\lambda$: Lagrangian, completely positive, and copositive relaxations. These relaxations are obtained by reducing the QOP to an equivalent QOP with a single quadratic equality constraint in nonnegative variables, … Read more