Christoph Neumann

Feasible rounding approaches and diving strategies in branch-and-bound methods for mixed-integer optimization

  • Christoph Neumann
  • Stefan Schwarze
  • Oliver Stein
  • Benjamin Müller
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Tags , , , , ,

    In this paper, we study the behavior of feasible rounding approaches for mixed-integer linear and nonlinear optimization problems (MILP and MINLP, respectively) when integrated into tree search of branch-and-bound. Our research addresses two important aspects. First, we develop insights into how an (enlarged) inner parallel set, which is the main component for feasible rounding approaches, … Read more

    Feasible rounding approaches for equality constrained mixed-integer optimization problems

  • Christoph Neumann
  • Oliver Stein
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Tags , , , ,

    A feasible rounding approach is a novel technique to compute good feasible points for mixed-integer optimization problems. The central idea of this approach is the construction of a continuously described inner parallel set for which any rounding of any of its elements is feasible in the original mixed-integer problem. It is known that this approach … Read more

    An explicit Tikhonov algorithm for nested variational inequalities

  • Lorenzo Lampariello
  • Christoph Neumann
  • Simone Sagratella
  • Oliver Stein
  • Jacopo Maria Ricci
    • Categories Complementarity and Variational Inequalities, Convex Optimization

    We consider nested variational inequalities consisting in a (upper-level) variational inequality whose feasible set is given by the solution set of another (lower-level) variational inequality. Purely hierarchical convex bilevel optimization problems and certain multi-follower games are particular instances of nested variational inequalities. We present an explicit and ready-to-implement Tikhonov-type solution method for such problems. We … Read more

    Equilibrium selection for multi-portfolio optimization

  • Lorenzo Lampariello
  • Christoph Neumann
  • Simone Sagratella
  • Oliver Stein
  • Jacopo Maria Ricci
    • Categories Complementarity and Variational Inequalities, Finance and Economics Tags , , , ,

    This paper studies a Nash game arising in portfolio optimization. We introduce a new general multi-portfolio model and state sufficient conditions for the monotonicity of the underlying Nash game. This property allows us to treat the problem numerically and, for the case of nonunique equilibria, to solve hierarchical problems of equilibrium selection. We also give … Read more

    Generating feasible points for mixed-integer convex optimization problems by inner parallel cuts

  • Christoph Neumann
  • Oliver Stein
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , ,

    In this article we introduce an inner parallel cutting plane method (IPCP) to compute good feasible points along with valid cutting planes for mixed-integer convex optimization problems. The method iteratively generates polyhedral outer approximations of an enlarged inner parallel set (EIPS) of the continuously relaxed feasible set. This EIPS possesses the crucial property that any … Read more

    Granularity in nonlinear mixed-integer optimization

  • Christoph Neumann
  • Oliver Stein
  • Nathan Sudermann-Merx
    • Categories (Mixed) Integer Nonlinear Programming

    We study a deterministic technique to check the existence of feasible points for mixed-integer nonlinear optimization problems which satisfy a structural requirement that we call granularity. We show that solving certain purely continuous optimization problems and rounding their optimal points leads to feasible points of the original mixed-integer problem, as long as the latter is … Read more

    A feasible rounding approach for mixed-integer optimization problems

  • Christoph Neumann
  • Oliver Stein
  • Nathan Sudermann-Merx
    • Categories (Mixed) Integer Linear Programming

    We introduce granularity as a sufficient condition for the consistency of a mixed-integer optimization problem, and show how to exploit it for the computation of feasible points: For optimization problems which are granular, solving certain linear problems and rounding their optimal points always leads to feasible points of the original mixed-integer problem. Thus, the resulting … Read more

    A feasible rounding approach for granular optimization problems

  • Christoph Neumann
  • Oliver Stein
  • Nathan Sudermann-Merx
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Tags , , , ,

    We introduce a new technique to generate good feasible points of mixed-integer nonlinear optimization problems. It makes use of the so-called inner parallel set of the relaxed feasible set, which was employed in O. Stein, Error bounds for mixed integer linear optimization problems, Mathematical Programming, Vol. 156 (2016), 101-123, as well as O. Stein, Error … Read more