error analysis

A proof for multilinear error bounds

  • Alberto Costa
    • Categories Nonlinear Optimization, Polyhedra Tags , , , ,

    \(\) We derive the error bounds for multilinear terms in $[0,1]^n$ using a proof methodology based on the polyhedral representation of the convex hull. We extend the result for multilinear terms in $[\boldsymbol{L},\boldsymbol{0}] \times [\boldsymbol{0},\boldsymbol{U}]\subset\mathbb{R}^n$. Article Download View A proof for multilinear error bounds

    Error bounds for monomial convexification in polynomial optimization

  • Warren Adams
  • Akshay Gupte
  • Yibo Xu
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory Tags , , , , ,

    Convex hulls of monomials have been widely studied in the literature, and monomial convexifications are implemented in global optimization software for relaxing polynomials. However, there has been no study of the error in the global optimum from such approaches. We give bounds on the worst-case error for convexifying a monomial over subsets of $[0,1]^n$. This … Read more