(Mixed) Integer Nonlinear Programming

Transmission and Generation Investment in Electricity Markets: The Effects of Market Splitting and Network Fee Regimes

  • Veronika Grimm
  • Martin Schmidt
  • Alexander Martin
  • Weibelzahl Martin
  • Gregor Zöttl
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Network Optimization Tags , , , , ,

    We propose an equilibrium model that allows to analyze the long-run impact of the regulatory environment on transmission line expansion by the regulator and investment in generation capacity by private firms in liberalized electricity markets. The model incorporates investment decisions of the transmission operator and private firms in expectation of an energy-only market and cost-based … Read more

    Computational Optimization of Gas Compressor Stations: MINLP Models vs. Continuous Reformulations

  • Daniel Rose
  • Martin Schmidt
  • Marc C. Steinbach
  • Bernhard M. Willert
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Nonlinear Optimization Tags , , , ,

    When considering cost-optimal operation of gas transport networks, compressor stations play the most important role. Proper modeling of these stations leads to complicated mixed-integer nonlinear and nonconvex optimization problems. In this article, we give an isothermal and stationary description of compressor stations, state MINLP and GDP models for operating a single station, and discuss several … Read more

    An Overview on Mathematical Programming Approaches for the Deterministic Unit Commitment Problem in Hydro Valleys

  • Claudia D'Ambrosio
  • Raouia Taktak
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences Tags , , ,

    With the fast-growing demand in the electricity market of the last decades, attention has been focused on alternative and flexible sources of energy such as hydro valleys. Managing the hydroelectricity produced by the plants in hydro valleys is called the hydro unit commitment problem. This problem consists in finding the optimal power production schedule of … Read more

    A polyhedral study of binary polynomial programs

  • Alberto Del Pia
  • Aida Khajavirad
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Global Optimization

    We study the polyhedral convex hull of a mixed-integer set S defined by a collection of multilinear equations over the 0-1-cube. Such sets appear frequently in the factorable reformulation of mixed-integer nonlinear optimization problems. In particular, the set S represents the feasible region of a linearized unconstrained binary polynomial optimization problem. We define an equivalent … Read more

    A Fast Branch-and-Bound Algorithm for Non-convex Quadratic Integer Optimization Subject To Linear Constraints Using Ellipsoidal Relaxations

  • Christoph Buchheim
  • Marianna De Santis
  • Laura Palagi
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Quadratic Programming

    We propose two exact approaches for non-convex quadratic integer minimization subject to linear constraints where lower bounds are computed by considering ellipsoidal relaxations of the feasible set. In the first approach, we intersect the ellipsoids with the feasible linear subspace. In the second approach we penalize exactly the linear constraints. We investigate the connection between … Read more

    LP formulations for mixed-integer polynomial optimization problems

  • Daniel Bienstock
  • Gonzalo Muñoz
    • Categories (Mixed) Integer Nonlinear Programming, Nonsmooth Optimization Tags

    We present polynomial-time algorithms for constrained optimization problems overwhere the intersection graph of the constraint set has bounded tree-width. In the case of binary variables we obtain exact, polynomial-size linear programming formulations for the problem. In the mixed-integer case with bounded variables we obtain polynomial-size linear programming representations that attain guaranteed optimality and feasibility bounds. … Read more

    Quadratic Cone Cutting Surfaces for Quadratic Programs with On-Off Constraints

  • Hyemin Jeon
  • Jeff Linderoth
  • Andrew J. Miller
    • Categories (Mixed) Integer Nonlinear Programming, Second-Order Cone Programming

    We study the convex hull of a set arising as a relaxation of difficult convex mixed integer quadratic programs (MIQP). We characterize the extreme points of our set and the extreme points of its continuous relaxation. We derive four quadratic cutting surfaces that improve the strength of the continuous relaxation. Each of the cutting surfaces … Read more

    Extended Formulations in Mixed Integer Conic Quadratic Programming

  • Iain Dunning
  • Joey Huchette
  • Juan Pablo Vielma
  • Miles Lubin
    • Categories (Mixed) Integer Nonlinear Programming

    In this paper we consider the use of extended formulations in LP-based algorithms for mixed integer conic quadratic programming (MICQP). Extended formulations have been used by Vielma, Ahmed and Nemhauser (2008) and Hijazi, Bonami and Ouorou (2013) to construct algorithms for MICQP that can provide a significant computational advantage. The first approach is based on … Read more

    Solving Power-Constrained Gas Transportation Problems using an MIP-based Alternating Direction Method

  • Björn Geißler
  • Antonio Morsi
  • Lars Schewe
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , , ,

    We present a solution algorithm for problems from steady-state gas transport optimization. Due to nonlinear and nonconvex physics and engineering models as well as discrete controllability of active network devices, these problems lead to hard nonconvex mixed-integer nonlinear optimization models. The proposed method is based on mixed-integer linear techniques using piecewise linear relaxations of the … Read more

    Convex hull of two quadratic or a conic quadratic and a quadratic inequality

  • Sina Modaresi
  • Juan Pablo Vielma
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory, Second-Order Cone Programming Tags , ,

    In this paper we consider an aggregation technique introduced by Yildiran, 2009 to study the convex hull of regions defined by two quadratic or by a conic quadratic and a quadratic inequality. Yildiran shows how to characterize the convex hull of open sets defined by two strict quadratic inequalities using Linear Matrix Inequalities (LMI). We … Read more