26 research outputs found
Mercado da energia eléctrica: uma modelação MPCC-NLP
O problema apresentado está relacionado com o
mercado de energia eléctrica, modelado como um jogo de Stackelberg, onde a empresa líder de mercado tem o poder de manipular os preços e a capacidade de produção, de forma a
maximizar o seu lucro. Devido às suas características particulares, o problema foi formulado como um Problema de Optimização com Restrições de Complementaridade (MPCC) e, posteriormente reestruturado num Problema de
Programação Não Linear (NLP), com o intuito de tirar partido das suas propriedades, utilizando software específico
A MPCC-NLP approach for an electric power market problem
The electric power market is changing - it has passed from a regulated market, where
the government of each country had the control of prices, to a deregulated market economy. Each company competes in order to get more clients and maximize its profits. This market is represented by a Stackelberg game with two firms, leader and follower, and the leader anticipates the reaction of the follower.
The problem is formulated as a Mathematical Program with Complementarity Constraints (MPCC). It is shown that the constraint qualifications usually assumed to prove convergence of standard algorithms fail to hold for MPCC. To circumvent this, a reformulation for a nonlinear problem (NLP) is proposed. Numerical tests using the NEOS server platform are presented
Mathematical programs with complementarity constraints: convergence properties of a smoothing method
In this paper, optimization problems with complementarity constraints are considered. Characterizations for local minimizers of of Orders 1 and 2 are presented. We analyze a parametric smoothing approach for solving these programs in which is replaced by a perturbed problem depending on a (small) parameter . We are interested in the convergence behavior of the feasible set and the convergence of the solutions of for In particular, it is shown that, under generic assumptions, the solutions are unique and converge to a solution of with a rate . Moreover, the convergence for the Hausdorff distance , between the feasible sets of and is of order
Solving Mathematical Programs with Equilibrium Constraints as Nonlinear Programming: A New Framework
We present a new framework for the solution of mathematical programs with
equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is
viewed as a concentration of an unconstrained optimization which minimizes the
complementarity measure and a nonlinear programming with general constraints. A
strategy generalizing ideas of Byrd-Omojokun's trust region method is used to
compute steps. By penalizing the tangential constraints into the objective
function, we circumvent the problem of not satisfying MFCQ. A trust-funnel-like
strategy is used to balance the improvements on feasibility and optimality. We
show that, under MPEC-MFCQ, if the algorithm does not terminate in finite
steps, then at least one accumulation point of the iterates sequence is an
S-stationary point