Hongyi Jiang

Information Complexity of Mixed-integer Convex Optimization

  • Amitabh Basu
  • Hongyi Jiang
  • Phillip Kerger
  • Marco Molinaro
    • Categories (Mixed) Integer Nonlinear Programming, Convex and Nonsmooth Optimization, Convex Optimization Tags , , ,

    We investigate the information complexity of mixed-integer convex optimization under different types of oracles. We establish new lower bounds for the standard first-order oracle, improving upon the previous best known lower bound. This leaves only a lower order linear term (in the dimension) as the gap between the lower and upper bounds. This is derived … Read more

    Complexity of cutting planes and branch-and-bound in mixed-integer optimization

  • Amitabh Basu
  • Michele Conforti
  • Marco Di Summa
  • Hongyi Jiang
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Cutting Plane Approaches Tags , ,

    We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency of BB and CP, when both are based on the same family of disjunctions. We extend a result of Dash to the nonlinear setting which shows that for convex 0/1 problems, CP … Read more