A Polyhedral Study of the Integrated Minimum-Up/-Down Time and Ramping Polytope

  • Yongpei Guan
  • Kai Pan
    • Categories Applications - Science and Engineering, Cutting Plane Approaches

    In this paper, we consider the polyhedral structure of the integrated minimum-up/-down time and ramping polytope for the unit commitment problem. Our studied generalized polytope includes minimum-up/-down time constraints, generation ramp-up/-down rate constraints, logical constraints, and generation upper/lower bound constraints. We derive strong valid inequalities by utilizing the structures of the unit commitment problem, and … Read more

    Embedding Formulations and Complexity for Unions of Polyhedra

  • Juan Pablo Vielma
    • Categories (Mixed) Integer Linear Programming

    It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is rarely a systematic construction leading to the best possible formulation. We introduce embedding formulations and complexity as a new MIP … Read more

    Perprof-py: a Python package for performance profile of mathematical optimization software

  • Luiz-Rafael Santos
  • Raniere Gaia Costa da Silva
  • Abel Soares Siqueira
    • Categories Optimization Software Benchmark

    A very important part of research in Mathematical Optimization field is to benchmark optimization packages because it is one of the ways to compare solvers. During benchmarking, one usually obtains a large amount of information, like CPU time, number of functions evaluations, number of iterations and much more. This information, if presented as tables, can … Read more

    Quadratically Perturbed Chance Constrained Programming with Fitted Distribution: t-Distribution vs. Gaussian

  • Xin He
    • Categories Stochastic Programming Tags , , ,

    For chance-constrained programming (CCP) with non-Gaussian uncertainty, the optimization is generally intractable owing to the complicated probability density function (PDF). Using a simple fitted distribution with Kullback-Leibler (KL) divergence to represent the PDF mismatch is a systematic way to tackle CCP with non-Gaussian uncertainty. However, the essential difficulty of this methodology is to choose the … Read more

    A Bundle Method for Exploiting Additive Structure in Difficult Optimization Problems

  • Welington de Oliveira
  • Jonathan Eckstein
    • Categories Convex Optimization, Nonsmooth Optimization

    This paper describes a bundle method for (approximately) minimizing complicated nonsmooth convex functions with additive structure, with the primary goal of computing bounds on the solution values of difficult optimization problems such as stochastic integer programs. The method combines features that have appeared in previously proposed bundle methods, but not in the particular configuration we … Read more

    New computer-based search strategies for extreme functions of the Gomory–Johnson infinite group problem

  • Matthias Köppe
  • Yuan Zhou
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , ,

    We describe new computer-based search strategies for extreme functions for the Gomory–Johnson infinite group problem. They lead to the discovery of new extreme functions, whose existence settles several open questions. Article Download View New computer-based search strategies for extreme functions of the Gomory–Johnson infinite group problem

    Regularization vs. Relaxation: A convexification perspective of statistical variable selection

  • Kun Chen
  • Hongbo Dong
  • Jeff Linderoth
    • Categories (Mixed) Integer Nonlinear Programming, Linear, Cone and Semidefinite Programming, Statistics Tags , , ,

    Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a quadratic optimization problem with an $\ell_0$-norm penalty. Exactly enforcing the $\ell_0$-norm penalty is computationally intractable for larger scale problems, so different sparsity-inducing penalty … Read more

    A Taxonomy of Constraints in Black-Box Simulation-Based Optimization

  • Sébastien Le Digabel
  • Stefan M. Wild
    • Categories Nonlinear Optimization, Optimization Software and Modeling Systems Tags , ,

    The types of constraints encountered in black-box simulation-based optimization problems differ significantly from those addressed in nonlinear programming. We introduce a characterization of constraints to address this situation. We provide formal definitions for several constraint classes and present illustrative examples in the context of the resulting taxonomy. This taxonomy, denoted KARQ, is useful for modeling … Read more

    A Theoretical and Algorithmic Characterization of Bulge Knees

  • Marlon Braun
  • Hartmut Schmeck
  • Pradyumn Kumar Shukla
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization

    This paper deals with the problem of finding convex bulges on the Pareto-front of a multi-objective optimization problem. The point of maximum bulge is of particular interest as this point shows good trade-off properties and it is also close to the non-attainable utopia point. Our approach is to use a population based algorithm to simultaneously … Read more