Analysis of Energy Markets Modeled as Equilibrium Problems with Equilibrium Constraints

  • Julia Filiberti
  • Steven A. Gabriel
  • Juan Pablo Luna
  • Claudia Sagastizábal
  • Mikhail V. Solodov
    • Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities, Nonsmooth Optimization Tags , ,

    Equilibrium problems with equilibrium constraints are challenging both theoretically and computationally. However, they are suitable/adequate modeling formulations in a number of important areas, such as energy markets, transportation planning, and logistics. Typically, these problems are characterized as bilevel Nash-Cournot games. For instance, determin- ing the equilibrium price in an energy market involves top-level decisions of … Read more

    Conflict Analysis for MINLP

  • Timo Berthold
  • Jakob Witzig
    • Categories (Mixed) Integer Nonlinear Programming

    The generalization of MIP techniques to deal with nonlinear, potentially non-convex, constraints have been a fruitful direction of research for computational MINLP in the last decade. In this paper, we follow that path in order to extend another essential subroutine of modern MIP solvers towards the case of nonlinear optimization: the analysis of infeasible subproblems … Read more

    Necessary and sufficient conditions for rank-one generated cones

  • C.J. Argue
  • Fatma Kılınç-Karzan
  • Alex L. Wang
    • Categories Quadratic Programming, Semi-definite Programming

    A closed convex conic subset $\cS$ of the positive semidefinite (PSD) cone is rank-one generated (ROG) if all of its extreme rays are generated by rank-one matrices. The ROG property of $\cS$ is closely related to the exactness of SDP relaxations of nonconvex quadratically constrained quadratic programs (QCQPs) related to $\cS$. We consider the case … Read more

    Benders decomposition for Network Design Covering Problems

  • Victor Bucarey
  • Bernard Fortz
  • Martine Labbé
  • Juan A. Mesa
  • Natividad González-Blanco
    • Categories Facility Planning and Design, Transportation Tags , , ,

    We consider two covering variants of the network design problem. We are given a set of origin/destination(O/D) pairs and each such O/D pair is covered if there exists a path in the network from the origin to the destination whose length is not larger than a given threshold. In the first problem, called the maximal … Read more

    Cut-Sharing Across Trees and Efficient Sequential Sampling for SDDP with Uncertainty in the RHS

  • Pedro Borges de Melo
    • Categories Dynamic Programming, Stochastic Programming

    In this paper we show that when a multistage stochastic problem with stage-wise independent realizations has only RHS uncertainties, solving one tree provides a valid lower bound for all trees with the same number of scenarios per stage without any additional computational effort. The only change to the traditional algorithm is the way cuts are … Read more

    Strong Formulations for Distributionally Robust Chance-Constrained Programs with Left-Hand Side Uncertainty under Wasserstein Ambiguity

  • Nam Ho-Nguyen
  • Fatma Kılınç-Karzan
  • Simge Küçükyavuz
  • Dabeen Lee
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    Distributionally robust chance-constrained programs (DR-CCP) over Wasserstein ambiguity sets exhibit attractive out-of-sample performance and admit big-$M$-based mixed-integer programming (MIP) reformulations with conic constraints. However, the resulting formulations often suffer from scalability issues as sample size increases. To address this shortcoming, we derive stronger formulations that scale well with respect to the sample size. Our focus … Read more

    The heterogeneous multicrew scheduling and routing problem in road restoration

  • Douglas Alem
  • Pedro Munari
  • Michel Gendreau
  • Alfredo Moreno
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization

    This paper introduces the heterogeneous multicrew scheduling and routing problem (MCSRP) in road restoration. The MCSRP consists of identifying the schedule and route of heterogeneous crews that must perform the restoration of damaged nodes used in the paths to connect a source node to demand nodes in a network affected by extreme events. The objective … Read more

    Characterization of an Anomalous Behavior of a Practical Smoothing Technique

  • Pedro Borges de Melo
    • Categories Game Theory, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    A practical smoothing method was analyzed and tested against state-of-the-art solvers for some non-smooth optimization problems in [BSS20a; BSS20b]. This method can be used to smooth the value functions and solution mappings of fully parameterized convex problems under mild conditions. In general, the smoothing of the value function lies from above the true value function … Read more

    Priority Based Flow Improvement with Intermediate Storage

  • Mohan Chandra Adhikari
  • Urmila Pyakurel
    • Categories Network Optimization Tags , , ,

    Every models in the network flow theory aim to increase flow value from the sources to the sinks and reduce time or cost satisfying the capacity and flow conservation constraints. Recently, the network flow model without flow conservation constraints at the intermediate nodes has been investigated by Pyakurel and Dempe \cite{pyadem:2019}. In this model, if … Read more

    Mathematical Programming formulations for the Alternating Current Optimal Power Flow problem

  • Daniel Bienstock
  • Mauro Escobar
  • Claudio Gentile
  • Leo Liberti
    • Categories Energy, Global Optimization Applications, Quadratic Programming Tags , ,

    Power flow refers to the injection of power on the lines of an electrical grid, so that all the injections at the nodes form a consistent flow within the network. Optimality, in this setting, is usually intended as the minimization of the cost of generating power. Current can either be direct or alternating: while the … Read more