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A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints

Name: A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints
Keywords: M-stationary points, Frechet normal cone, limiting normal cone, S-stationary points, mathematical programs with equilibrium constraints

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2010 Czech Republic English

Authors: Outrata, J. (Jiří); Henrion, R.; Surowiec, T.;

handle: 11104/0186313

A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints

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Abstract

In this paper, we deal with strong stationarity conditions for mathematical programs with equilibrium constraints (MPEC). The main task in deriving these conditions consists in calculating the Fr´echet normal cone to the graph of the solution mapping associated with the underlying generalized equation of the MPEC. We derive an inner approximation to this cone, which is exact under an additional assumption. Even if the latter fails to hold, the inner approximation can be used to check strong stationarity via the weaker (but easier to calculate) concept of M-stationarity.

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Czech Republic

Related Organizations

Czech Academy of Sciences
Czech Republic
Academy of Sciences Library
Czech Republic

Keywords

M-stationary points, Frechet normal cone, limiting normal cone, S-stationary points, mathematical programs with equilibrium constraints

7 Research products, page 1 of 1

Stability Analysis for Parametric Mathematical Programs with Geometric Constraints and Its Applications
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On Stability of M-stationary Points in MPCCs
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Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market
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Enhanced Fritz John stationarity, new constraint qualifications and local error bound for mathematical programs with vanishing constraints
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On M-stationary points for mathematical programs with equilibrium constraints
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A new elementary proof for M-stationarity under MPCC-GCQ for mathematical programs with complementarity constraints
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A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints
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A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints

A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints

7 Research products, page 1 of 1

Stability Analysis for Parametric Mathematical Programs with Geometric Constraints and Its Applications

On Stability of M-stationary Points in MPCCs

Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market

Enhanced Fritz John stationarity, new constraint qualifications and local error bound for mathematical programs with vanishing constraints

On M-stationary points for mathematical programs with equilibrium constraints

A new elementary proof for M-stationarity under MPCC-GCQ for mathematical programs with complementarity constraints

A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints