Juan Pablo Luna

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

    A DISCUSSION ON ELECTRICITY PRICES, OR THE TWO SIDES OF THE COIN

  • Juan Pablo Luna
  • Claudia Sagastizábal
  • Paulo J. S. Silva
    • Categories Applications - OR and Management Sciences, Nonlinear Optimization Tags , , ,

    We examine how different pricing frameworks deal with nonconvex features typical of day-ahead energy prices when the power system is hydro-dominated, like in Brazil. For the system operator, requirements of minimum generation translate into feasibility issues that are fundamental to carry the generated power through the network. When utilities are remunerated at a price depending … Read more

    An approximation scheme for a class of risk-averse stochastic equilibrium problems

  • Juan Pablo Luna
  • Claudia Sagastizábal
  • Mikhail V. Solodov
    • Categories Complementarity and Variational Inequalities, Stochastic Programming Tags , , , , ,

    We consider two models for stochastic equilibrium: one based on the variational equilibrium of a generalized Nash game, and the other on the mixed complementarity formulation. Each agent in the market solves a one-stage risk-averse optimization problem with both here-and-now (investment) variables and (production) wait-and-see variables. A shared constraint couples almost surely the wait-and-see decisions … Read more

    A Class of Dantzig-Wolfe Type Decomposition Methods for Variational Inequality Problems

  • Juan Pablo Luna
  • Claudia Sagastizábal
  • Mikhail V. Solodov
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization Tags ,

    We consider a class of decomposition methods for variational inequalities, which is related to the classical Dantzig–Wolfe decomposition of linear programs. Our approach is rather general, in that it can be used with set-valued or nonmonotone operators, as well as various kinds of approximations in the subproblems of the functions and derivatives in the single-valued … Read more