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

    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

    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

    Maximizing a class of submodular utility functions with constraints

  • Shabbir Ahmed
  • Jiajin Yu
    • Categories 0-1 Programming, Cutting Plane Approaches, Stochastic Programming Tags , , , ,

    Motivated by stochastic 0-1 integer programming problems with an expected utility objective, we study the mixed-integer nonlinear set: $P = \cset{(w,x)\in \reals \times \set{0,1}^N}{w \leq f(a’x + d), b’x \leq B}$ where $N$ is a positive integer, $f:\reals \mapsto \reals$ is a concave function, $a, b \in \reals^N$ are nonnegative vectors, $d$ is a real … Read more

    A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in n-space

  • Marcia Fampa
  • Jon Lee
  • Wendel Melo
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms Tags , , ,

    We present a specialized branch-and-bound (b&b) algorithm for the Euclidean Steiner tree problem (ESTP) in R^n and apply it to a convex mixed-integer nonlinear programming (MINLP) formulation of the problem, presented by Fampa and Maculan. The algorithm contains procedures to avoid difficulties observed when applying a b&b algorithm for general MINLP problems to solve the … Read more

    On a nonconvex MINLP formulation of the Euclidean Steiner tree problems in n-space

  • Claudia D'Ambrosio
  • Marcia Fampa
  • Jon Lee
  • Stefan Vigerske
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization, Global Optimization Tags , ,

    The Euclidean Steiner Tree Problem in dimension greater than two is notoriously difficult. The successful methods for exact solution are not based on mathematical-optimization methods — rather, they involve very sophisticated enumeration. There are two types of mathematical-optimization formulations in the literature, and it is an understatement to say that neither scales well enough to … Read more

    Constraint Qualification Failure in Action

  • Hassan L. Hijazi
  • Leo Liberti
    • Categories (Mixed) Integer Nonlinear Programming, Second-Order Cone Programming Tags , , , ,

    This note presents a theoretical analysis of disjunctive constraints featuring unbounded variables. In this framework, classical modeling techniques, including big-M approaches, are not applicable. We introduce a lifted second-order cone formulation of such on/off constraints and discuss related constraint qualification issues. A solution is proposed to avoid solvers’ failure. Citation H. L. Hijazi and L.Liberti … Read more

    How to Convexify the Intersection of a Second Order Cone and a Nonconvex Quadratic

  • Samuel Burer
  • Fatma Kılınç-Karzan
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory, Second-Order Cone Programming Tags , , , , , , ,

    A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown—by several authors using different techniques—that the convex hull of the intersection of an ellipsoid, $\E$, and a split disjunction, $(l – x_j)(x_j – u) \le 0$ with $l < u$, equals the intersection ... Read more

    Mathematical Programming techniques in Water Network Optimization

  • Cristiana Bragalli
  • Claudia D'Ambrosio
  • Andrea Lodi
  • Sven Wiese
    • Categories (Mixed) Integer Nonlinear Programming, Civil and Environmental Engineering Tags , , ,

    In this article we survey mathematical programming approaches to problems in the field of water network optimization. Predominant in the literature are two different, but related problem classes. One can be described by the notion of network design, while the other is more aptly termed by network operation. The basic underlying model in both cases … Read more

    Cutting Planes for RLT Relaxations of Mixed 0-1 Polynomial Programs

  • Franklin Djeumou Fomeni
  • Konstantinos Kaparis
  • Adam N. Letchford
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Tags , ,

    The Reformulation-Linearization Technique (RLT), due to Sherali and Adams, can be used to construct hierarchies of linear programming relaxations of mixed 0-1 polynomial programs. As one moves up the hierarchy, the relaxations grow stronger, but the number of variables increases exponentially. We present a procedure that generates cutting planes at any given level of the … Read more