What question did this study set out to answer?

To analyze the theoretical properties, local solution existence, and error bounds of regularized and penalized formulations of mathematical programs with equilibrium constraints (MPECs).

August 17, 2004Optimization methods & software

Some properties of regularization and penalization schemes for MPECs

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To analyze the theoretical properties, local solution existence, and error bounds of regularized and penalized formulations of mathematical programs with equilibrium constraints (MPECs).
Analyzed regularized MPEC formulations where complementarity constraints are substituted with constraints governed by a positive parameter driven toward zero.
Evaluated penalized MPEC formulations that incorporate complementarity conditions directly into the objective function as penalty terms.
Examined local behavior around solutions satisfying strong stationarity and second-order sufficient conditions.
Established the existence and local uniqueness of solutions for both regularized and penalized MPEC formulations.
Derived quantitative distance estimates between approximate formulation solutions and true local MPEC solutions under varying structural assumptions.

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Implication

Theoretical analysis demonstrates solution existence and convergence bounds for regularized and penalized MPECs, highlighting improved stability near equilibrium points.

Cite This Study

Ralph et al. (2004) studied this question.

synapsesocial.com/papers/6a1c6b1a66d062ff2dc3c99b https://doi.org/10.1080/10556780410001709439

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Implication

Theoretical analysis demonstrates solution existence and convergence bounds for regularized and penalized MPECs, highlighting improved stability near equilibrium points.

Some properties of regularization and penalization schemes for MPECs

Key Points

Discussion

Implication

Cite This Study

Some properties of regularization and penalization schemes for MPECs

Key Points

Discussion

Implication

Cite This Study

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