An MPEC reformulation of an EPEC model for electricity markets

Guo, Lei; Lin, Guo; Zhang, Dali; Zhu, Daoli

doi:10.1016/j.orl.2015.03.001

Cited by 27 publications

(17 citation statements)

References 15 publications

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“…MPCCs are also present in many applications like urban traffic control, economy, problems arising from the electrical sector, etc. See [18,25,41,42,51] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Convergence Properties of a Second Order Augmented Lagrangian Method for Mathematical Programs with Complementarity Constraints

Andreani¹,

Secchin²,

Silva³

2018

SIAM J. Optim.

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Mathematical Programs with Complementarity Constraints (MPCCs) are difficult optimization problems that do not satisfy the majority of the usual constraint qualifications (CQs) for standard nonlinear optimization. Despite this fact, classical methods behaves well when applied to MPCCs. Recently, Izmailov, Solodov and Uskov proved that first order augmented Lagrangian methods, under a natural adaption of the Linear Independence Constraint Qualification to the MPCC setting (MPCC-LICQ), converge to strongly stationary (S-stationary) points, if the multiplier sequence is bounded. If the multiplier sequence is not bounded, only Clarke stationary (C-stationary) points are recovered. In this paper we improve this result in two ways. For the case of bounded multipliers we are able replace the MPCC-LICQ assumption by the much weaker MPCC-Relaxed Positive Linear Dependence condition (MPCC-RCLPD). For the case with unbounded multipliers, building upon results from Scholtes, Anitescu, and others, we show that a second order augmented Lagrangian method converges to points that are at least Mordukhovich stationary (M-stationary) but we still need the more stringent MPCC-LICQ assumption. Numerical tests, validating the theory, are also presented.

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“…MPCCs are also present in many applications like urban traffic control, economy, problems arising from the electrical sector, etc. See [18,25,41,42,51] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Convergence Properties of a Second Order Augmented Lagrangian Method for Mathematical Programs with Complementarity Constraints

Andreani¹,

Secchin²,

Silva³

2018

SIAM J. Optim.

View full text Add to dashboard Cite

show abstract

“…Separability assumption of the EPEC model is also different from the ones studied in [7,8] and [16].…”

Section: Introductionmentioning

confidence: 94%

“…They also reformulated price-consistent multi-leader-follower game to a standard MPEC by imposing an additional restriction. See also various applications in economics such as Ehrenmann [2], Ehrenmann and Neuho [3], Hu [12], Murphy and Smeers [17], Su [22], Yao et al [23]; and the algorithm investigation Su [21].Guo and Lin [7,8] reformulated various stationarities for EPECs as constrained equations and proposed a globally and superlinearly convergent algorithm to solve these constrained equations. Li [16] considered a class of EPECs which is completely separable.…”

Section: Introductionmentioning

confidence: 99%

Solving a Class of Equilibrium Problems With Equilibrium Constraints*

Li¹,

Ding²

2021

Preprint

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An equilibrium problem with equilibrium constraints (EPEC) can be looked on as a generalized Nash equilibrium problem (GNEP) and the mathematical programs with equilibrium constraints (MPEC) whose constraints contain a parametric variational inequality or complementarity system. In this paper, we particularly consider a class of EPEC and solve its normalized stationary points where the multipliers of the leaders on the shared constraints are proportionable. We reformulate this kind of EPEC to a standard MPEC. In addition, we demonstrate the proposed approach on an EPEC model in similar products market.

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“…The upper-level problem allows the agent to determine its best offering/bidding strategy (to be transferred to the lowerlevel problem), while the lower-level problem provides the market clearing price (as a dual variable) needed to compute the agent's profit at the upper-level problem. Further details are provided in [5], [3], [6] and [7]. The lower-level problem (inner box of the lower box of Fig.…”

Section: Strategic Agentsmentioning

confidence: 99%

Complementarity, Not Optimization, is the Language of Markets

Conejo

Ruiz

2020

IEEE Open J. Power Energy

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Each market agent (producer or consumer) in a power market pursues its own objective, typically to maximize its own profit. As such, the specific behavior of each agent in the market is conveniently formulated as a bi-level optimization problem whose upper-level problem represents the profit seeking behavior of the agent and whose lower-level problem represents the clearing of the market. The objective function and the constraints of this bi-level problem depend on the agent's own decision variables and on those of other agents as well. Understanding the outcomes of the market requires considering and solving jointly the interrelated bi-level problems of all market agents, which is beyond the purview of optimization. Solving jointly a set of bi-level (or single-level) optimization problems that are interrelated is the purview of complementarity. In this paper and in the context of power markets, we review complementarity using a tutorial approach.

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An MPEC reformulation of an EPEC model for electricity markets

Cited by 27 publications

References 15 publications

Convergence Properties of a Second Order Augmented Lagrangian Method for Mathematical Programs with Complementarity Constraints

Convergence Properties of a Second Order Augmented Lagrangian Method for Mathematical Programs with Complementarity Constraints

Solving a Class of Equilibrium Problems With Equilibrium Constraints*

Complementarity, Not Optimization, is the Language of Markets

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