Gabriele Eichfelder

On implementation details and numerical experiments for the HyPaD algorithm to solve multi-objective mixed-integer convex optimization problems

  • Gabriele Eichfelder
  • Leo Warnow
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , ,

    In this paper we present insights on the implementation details of the hybrid patch decomposition algorithm (HyPaD) for convex multi-objective mixed-integer optimization problems. We discuss how to implement the SNIA procedure which is basically a black box algorithm in the original work by Eichfelder and Warnow. In addition, we present and discuss results for various … Read more

    A Vectorization Scheme for Nonconvex Set Optimization Problems

  • Gabriele Eichfelder
  • Ernest Quintana
  • Stefan Rocktäschel
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization Tags , , , ,

    In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from multiobjective optimization. Our strategy consists of deriving a parametric family of multiobjective optimization problems whose optimal solution … Read more

    Limit sets in global multiobjective optimization

  • Gabriele Eichfelder
  • Oliver Stein
    • Categories Global Optimization Theory, Multi-Criteria Optimization Tags , , , , ,

    Inspired by the recently introduced branch-and-bound method for continuous multiobjective optimization problems from G. Eichfelder, P. Kirst, L. Meng, O. Stein, A general branch-and-bound framework for continuous global multiobjective optimization, Journal of Global Optimization, 80 (2021) 195-227, we study for a general class of branch-and-bound methods in which sense the generated terminal enclosure and the … Read more

    Solving set-valued optimization problems using a multiobjective approach

  • Gabriele Eichfelder
  • Stefan Rocktäschel
    • Categories Multi-Criteria Optimization, Robust Optimization Tags , , ,

    Set-valued optimization using the set approach is a research topic of high interest due to its practical relevance and numerous interdependencies to other fields of optimization. However, it is a very difficult task to solve these optimzation problems even for specific cases. In this paper we study set-valued optimization problems and develop a multiobjective optimization … Read more

    Twenty years of continuous multiobjective optimization in the twenty-first century

  • Gabriele Eichfelder
    • Categories Global Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    The survey highlights some of the research topics which have attracted attention in the last two decades within the area of mathematical optimization of multiple objective functions. We give insights into topics where a huge progress can be seen within the last years. We give short introductions to the specific sub-fields as well as some … Read more

    An approximation algorithm for multi-objective optimization problems using a box-coverage

  • Gabriele Eichfelder
  • Leo Warnow
    • Categories Global Optimization, Multi-Criteria Optimization Tags , , , ,

    For a continuous multi-objective optimization problem, it is usually not a practical approach to compute all its nondominated points because there are infinitely many of them. For this reason, a typical approach is to compute an approximation of the nondominated set. A common technique for this approach is to generate a polyhedron which contains the … Read more

    A general branch-and-bound framework for continuous global multiobjective optimization

  • Gabriele Eichfelder
  • Peter Kirst
  • Oliver Stein
  • Laura Meng
    • Categories Global Optimization, Multi-Criteria Optimization, Nonlinear Optimization

    Current generalizations of the central ideas of single-objective branch-and-bound to the multiobjective setting do not seem to follow their train of thought all the way. The present paper complements the various suggestions for generalizations of partial lower bounds and of overall upper bounds by general constructions for overall lower bounds from partial lower bounds, and … Read more

    A Decision Space Algorithm for Multiobjective Convex Quadratic Integer Optimization

  • Marianna De Santis
  • Gabriele Eichfelder
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , , ,

    We present a branch-and-bound algorithm for minimizing multiple convex quadratic objective functions over integer variables. Our method looks for efficient points by fixing subsets of variables to integer values and by using lower bounds in the form of hyperplanes in the image space derived from the continuous relaxations of the restricted objective functions. We show … Read more

    Optimality conditions in discrete-continuous nonlinear optimization

  • Gabriele Eichfelder
  • Johannes Jahn
    • Categories (Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization

    This paper presents necessary and sufficient optimality conditions for discrete-continuous nonlinear optimization problems including mixed-integer nonlinear problems. This theory does not utilize an extension of the Lagrange theory of continuous optimization but it works with certain max functionals for a separation of two sets where one of them is nonconvex. These functionals have the advantage … Read more

    Nonconvex Constrained Optimization by a Filtering Branch and Bound

  • Gabriele Eichfelder
  • Kathrin Klamroth
  • Julia Niebling
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Multi-Criteria Optimization

    A major difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the alphaBB-algorithm for single-objective optimization may fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In this work, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained … Read more