Chris Coey

Towards practical generic conic optimization

  • Chris Coey
  • Juan Pablo Vielma
  • Lea Kapelevich
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , , ,

    Many convex optimization problems can be represented through conic extended formulations with auxiliary variables and constraints using only the small number of standard cones recognized by advanced conic solvers such as MOSEK 9. Such extended formulations are often significantly larger and more complex than equivalent conic natural formulations, which can use a much broader class … Read more

    Outer Approximation With Conic Certificates For Mixed-Integer Convex Problems

  • Chris Coey
  • Miles Lubin
  • Juan Pablo Vielma
    • Categories (Mixed) Integer Nonlinear Programming, Linear, Cone and Semidefinite Programming, Optimization Software Benchmark Tags , ,

    A mixed-integer convex (MI-convex) optimization problem is one that becomes convex when all integrality constraints are relaxed. We present a branch-and-bound LP outer approximation algorithm for an MI-convex problem transformed to MI-conic form. The polyhedral relaxations are refined with K* cuts} derived from conic certificates for continuous primal-dual conic subproblems. Under the assumption that all … Read more