Daniel Ralph

Open versus closed loop capacity equilibria in electricity markets under perfect and oligopolistic competition

  • Julian Barquín
  • Daniel Ralph
  • E. Centeno
  • Benjamin Hobbs
  • S. Wogrin
    • Categories Applications - OR and Management Sciences, Game Theory

    We consider two game-theoretic models of the generation capacity expansion problem in liberalized electricity markets. The first is an open loop equilibrium model, where generation companies simultaneously choose capacities and quantities to maximize their individual profit. The second is a closed loop model, in which companies first choose capacities maximizing their profit anticipating the market … Read more

    A Constructive Proof of the Existence of a Utility in Revealed Preference Theory

  • J-P Crouzeix
  • Andrew C. Eberhard
  • Daniel Ralph
    • Categories Approximation Algorithms, Finance and Economics, Generalized Convexity/Monoticity Tags , ,

    Within the context of the standard model of rationality within economic modelling we show the existence of a utility function that rationalises a demand correspondence, hence completely characterizes the associated preference structure, by taking a dense demand sample. This resolves the problem of revealed preferences under some very mild assumptions on the demand correspondence which … Read more

    Multiplier convergence in trust-region methods with application to convergence of decomposition methods for MPECs

  • Giovanni Giallombardo
  • Daniel Ralph
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , , ,

    We study piecewise decomposition methods for mathematical programs with equilibrium constraints (MPECs) for which all constraint functions are linear. At each iteration of a decomposition method, one step of a nonlinear programming scheme is applied to one piece of the MPEC to obtain the next iterate. Our goal is to understand global convergence to B-stationary … Read more

    Using EPECs to model bilevel games in restructured electricity markets

  • Xinmin Hu
  • Daniel Ralph
    • Categories Complementarity and Variational Inequalities, Finance and Economics Tags , , , , ,

    We study a bilevel noncooperative game-theoretic model of restructured electricity markets, with locational marginal prices. Each player in this game faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. The corresponding game is an example of an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for … Read more

    Efficient Robust Optimization for Robust Control with Constraints

  • Paul J. Goulart
  • Daniel Ralph
  • EC Kerrigan
    • Categories Control Applications, Robust Optimization Tags , , , , ,

    This paper proposes an efficient computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with mixed polytopic constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is non-convex. A recent breakthrough has been the application of robust optimization techniques … Read more

    Some Properties of Regularization and Penalization Schemes for MPECs

  • Daniel Ralph
  • Stephen Wright
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , ,

    Some properties of regularized and penalized nonlinear programming formulations of mathematical programs with equilibrium constraints (MPECs) are described. The focus is on the properties of these formulations near a local solution of the MPEC at which strong stationarity and a second-order sufficient condition are satisfied. In the regularized formulations, the complementarity condition is replaced by … Read more

    Convergence of a Penalty Method for Mathematical Programmingwith ComplementarityConstraints

  • Xinmin Hu
  • Daniel Ralph
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , ,

    We adapt the convergence analysis of smoothing (Fukushima and Pang) and regularization (Scholtes) methods to a penalty framework for mathematical programs with complementarity constraints (MPCCs), and show that the penalty framework shares similar convergence properties to these methods. Moreover, we give sufficient conditions for a sequence generated by the penalty framework to be attracted to … Read more

    A stable homotopy approach to horizontal linear complementarity problems

  • Daniel Ralph
    • Categories Complementarity and Variational Inequalities Tags , , , , , , , , , , , ,

    We are interested in the solution of Horizontal Linear Complementarity Problems, HLCPs, that is complementarity problems with more variables than equations. Globally metrically regular HLCPs have nonempty solution sets that are stable with respect to “right-hand-side perturbations” of the data, hence are numerically attractive. The main purpose of the paper is to show how the … Read more

    Extension of Quasi-Newton Methods to Mathematical Programs with Complementarity Constraints

  • Houyuan Jiang
  • Daniel Ralph
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , , , ,

    Quasi-Newton methods in conjunction with the piecewise sequential quadratic programming are investigated for solving mathematical programming with equilibrium constraints, in particular for problems with complementarity constraints. Local convergence as well as superlinear convergence of these quasi-Newton methods can be established under suitable assumptions. In particular, several well-known quasi-Newton methods such as BFGS and DFP are … Read more

    Local convergence of SQP methods for Mathematical Programs with Equilibrium Constraints

  • Roger Fletcher
  • Sven Leyffer
  • Daniel Ralph
  • Stefan Scholtes
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , ,

    Recently, it has been shown that Nonlinear Programming solvers can successfully solve a range of Mathematical Programs with Equilibrium Constraints (MPECs). In particular, Sequential Quadratic Programming (SQP) methods have been very successful. This paper examines the local convergence properties of SQP methods applied to MPECs. It is shown that SQP converges superlinearly under reasonable assumptions … Read more