(Mixed) Integer Nonlinear Programming

Solving Binary-Constrained Mixed Complementarity Problems Using Continuous Reformulations

  • Steven A. Gabriel
  • Martin Schmidt
  • Marina Leal
    • Categories (Mixed) Integer Nonlinear Programming, Complementarity and Variational Inequalities, Transportation Tags , , ,

    Mixed complementarity problems are of great importance in practice since they appear in various fields of applications like energy markets, optimal stopping, or traffic equilibrium problems. However, they are also very challenging due to their inherent, nonconvex structure. In addition, recent applications require the incorporation of integrality constraints. Since complementarity problems often model some kind … Read more

    Mixed-Integer Optimal Control Problems with switching costs: A shortest path approach

  • Felix Bestehorn
  • Christoph Hansknecht
  • Christian Kirches
  • Paul Manns
    • Categories (Mixed) Integer Nonlinear Programming, Approximation Algorithms Tags , , , ,

    We investigate an extension of Mixed-Integer Optimal Control Problems (MIOCPs) by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the … Read more

    Quantum Bridge Analytics II: Network Optimization and Combinatorial Chaining for Asset Exchange

  • Yu Du
  • Fred Glover
  • Gary Kochenberger
  • Moses Ma
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization, Network Optimization Tags , , , , ,

    Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing, and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the second of a two-part tutorial that surveys … Read more

    A Finitely Convergent Disjunctive Cutting Plane Algorithm for Bilinear Programming

  • Hamed Rahimian
  • Sanjay Mehrotra
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Quadratic Programming Tags , , , ,

    In this paper we present and analyze a finitely-convergent disjunctive cutting plane algorithm to obtain an \(\epsilon\)-optimal solution or detect infeasibility of a general nonconvex continuous bilinear program. While the cutting planes are obtained in a manner similar to Saxena, Bonami, and Lee [Math. Prog. 130: 359–413, 2011] and Fampa and Lee [J. Global Optim. … Read more

    Sequential Convexification of a Bilinear Set

  • Hamed Rahimian
  • Sanjay Mehrotra
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , , , ,

    We present a sequential convexification procedure to derive, in the limit, a set arbitrary close to the convex hull of $\epsilon$-feasible solutions to a general nonconvex continuous bilinear set. Recognizing that bilinear terms can be represented with a finite number nonlinear nonconvex constraints in the lifted matrix space, our procedure performs a sequential convexification with … Read more

    A Mixed-Integer PDE-Constrained Optimization Formulation for Electromagnetic Cloaking

  • Sven Leyffer
  • Todd S. Munson
  • Ryan Vogt
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Optimization of Systems modeled by PDEs Tags , , ,

    We formulate a mixed-integer partial-differential equation constrained optimization problem for designing an electromagnetic cloak governed by the 2D Helmholtz equation with absorbing boundary conditions. Our formulation is an alternative to the topology optimization formulation of electromagnetic cloaking design. We extend the formulation to include uncertainty with respect to the angle of the incidence wave, and … Read more

    On the convexification of constrained quadratic optimization problems with indicator variables

  • Andrés Gómez
  • Simge Küçükyavuz
  • Linchuan Wei
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , , , ,

    Motivated by modern regression applications, in this paper, we study the convexification of quadratic optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work on convexification of sparse regression problems, we simultaneously consider the nonlinear objective, indicator variables, and combinatorial constraints. We prove that for a separable quadratic … Read more

    Stochastic Dual Dynamic Programming for Multistage Stochastic Mixed-Integer Nonlinear Optimization

  • Shixuan Zhang
  • Xu Andy Sun
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Stochastic Programming Tags , , ,

    In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with \emph{non-Lipschitz-continuous} value functions and multistage stochastic mixed-integer linear optimization. We develop stochastic dual dynamic programming (SDDP) type algorithms with nested decomposition, deterministic sampling, and stochastic sampling. The key ingredient … Read more

    Outer Approximation for Global Optimization of Mixed-Integer Quadratic Bilevel Problems

  • Veronika Grimm
  • Thomas Kleinert
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , , ,

    Bilevel optimization problems have received a lot of attention in the last years and decades. Besides numerous theoretical developments there also evolved novel solution algorithms for mixed-integer linear bilevel problems and the most recent algorithms use branch-and-cut techniques from mixed-integer programming that are especially tailored for the bilevel context. In this paper, we consider MIQP-QP … Read more