mixed-integer nonlinear programming

AI for Enhancing Operations Research of Agriculture and Energy

  • Morteza Kimiaei
  • Anshu Kumar
  • Vyacheslav Kungurtsev
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , , , , ,

    This paper surveys optimization problems arising in agriculture, energy systems, and water-energy coordination from an operations research perspective. These problems are commonly formulated as integer nonlinear programs, mixed-integer nonlinear programs, or combinatorial set optimization models, characterized by nonlinear physical constraints, discrete decisions, and intertemporal coupling. Such structures pose significant computational challenges in large-scale and repeated-solution … Read more

    Semidefinite programming via Projective Cutting Planes for dense (easily-feasible) instances

  • Daniel Porumbel
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , ,

    The cone of positive semi-definite (SDP) matrices can be described by an infinite number of linear constraints. It is well-known that one can optimize over such a feasible area by standard Cutting Planes, but work on this idea remains a rare sight, likely due to its limited practical appeal compared to Interior Point Methods (IPMs). … Read more

    The SCIP Optimization Suite 10.0

  • Christopher Hojny
  • Mathieu Besançon
  • Ksenia Bestuzheva
  • Sander Borst
  • Antonia Chmiela
  • João Dionísio
  • Leon Eifler
  • Mohammed Ghannam
  • Ambros Gleixner
  • Adrian Göß
  • Alexander Hoen
  • Rolf van der Hulst
  • Dominik Kamp
  • Thorsten Koch
  • Kevin Kofler
  • Jurgen Lentz
  • Stephen J. Maher
  • Gioni Mexi
  • Erik Mühmer
  • Marc E. Pfetsch
  • Sebastian Pokutta
  • Felipe Serrano
  • Yuji Shinano
  • Mark Turner
  • Stefan Vigerske
  • Matthias Walter
  • Dieter Weninger
  • Liding Xu
    • Categories Integer Programming, Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , , , , , , , , ,

    The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in SCIP Optimization Suite 10.0. The updates in SCIP 10.0 include a new solving mode for exactly solving rational mixed-integer linear programs, a new presolver … Read more

    Randomized Roundings for a Mixed-Integer Elliptic Control System

  • Martin T. Köhler
  • Lauri Kröger
  • Christian Kirches
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , ,

    We present randomized reconstruction approaches for optimal solutions to mixed-integer elliptic PDE control systems. Approximation properties and relations to sum-up rounding are derived using the cut norm. This enables us to dispose of space-filling curves required for sum-up rounding. Rates of almost sure convergence in the cut norm and the SUR norm in control space … Read more

    Granularity for mixed-integer polynomial optimization problems

  • Carl Eggen
  • Oliver Stein
  • Stefan Volkwein
    • Categories (Mixed) Integer Nonlinear Programming, Semi-definite Programming Tags , , , ,

    Finding good feasible points is crucial in mixed-integer programming. For this purpose we combine a sufficient condition for consistency, called granularity, with the moment-/sos-hierarchy from polynomial optimization. If the mixed-integer problem is granular, we obtain feasible points by solving continuous polynomial problems and rounding their optimal points. The moment-/sos-hierarchy is hereby used to solve those … Read more

    An outer approximation method for solving mixed-integer convex quadratic programs with indicators

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

    Mixed-integer convex quadratic programs with indicator variables (MIQP) encompass a wide range of applications, from statistical learning to energy, finance, and logistics. The outer approximation (OA) algorithm has been proven efficient in solving MIQP, and the key to the success of an OA algorithm is the strength of the cutting planes employed. In this paper, … Read more

    Benchmarking Piecewise Linear Reformulations for MINLPs: A Computational Study Based on the Open-Source Framework PWL-T-Rex

  • Kristin Braun
  • Robert Burlacu
    • Categories (Mixed) Integer Nonlinear Programming Tags , , ,

    Solving mixed-integer nonlinear problems by means of piecewise linear relaxations has emerged as a reasonable alternative to the commonly used spatial branch-and-bound. These relaxations have been modeled by various mixed-integer models in recent decades. The idea is to exploit the availability of mature solvers for mixed-integer problems. In this work, we implement a framework that … Read more

    Global Optimization of Mixed-Integer Nonlinear Programs with SCIP 8.0

  • Ksenia Bestuzheva
  • Antonia Chmiela
  • Benjamin Müller
  • Felipe Serrano
  • Stefan Vigerske
  • Fabian Wegscheider
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Optimization Software and Modeling Systems Tags , , ,

    For over ten years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that … Read more

    Computing an enclosure for multiobjective mixed-integer nonconvex optimization problems using piecewise linear relaxations

  • Moritz Link
  • Stefan Volkwein
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization, Network Optimization Tags , , , ,

    In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer problems without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonconvexity of the original problem. The method chooses adaptively which level of relaxation is … Read more

    New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation

  • Loay Alkhalifa
  • Hans D Mittelmann
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform … Read more