# On the Karush–Kuhn–Tucker reformulation of the bilevel optimization problem

@inproceedings{Dempe2012OnTK, title={On the Karush–Kuhn–Tucker reformulation of the bilevel optimization problem}, author={Stephan Dempe and Alain B. Zemkoho}, year={2012} }

This paper is mainly concerned with the classical KKT reformulation and the primal KKT reformulation (also known as an optimization problem with generalized equation constraint (OPEC)) of the optimistic bilevel optimization problem. A generalization of the MFCQ to an optimization problem with operator constraint is applied to each of these reformulations, hence leading to new constraint qualifications (CQs) for the bilevel optimization problem. M- and S-type stationarity conditions tailored for… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 44 REFERENCES

## Variational analysis and generalized differentiation

VIEW 15 EXCERPTS

HIGHLY INFLUENTIAL

## Constraint qualification and stationarity concepts for mathematical programs with equilibrium constraints

VIEW 12 EXCERPTS

HIGHLY INFLUENTIAL

## Lipschitz Behavior of Solutions to Convex Minimization Problems

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Optimality conditions for bilevel programming problems

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity

VIEW 11 EXCERPTS

HIGHLY INFLUENTIAL

## Variational Analysis

VIEW 11 EXCERPTS

HIGHLY INFLUENTIAL

## Exact Penalization and Necessary Optimality Conditions for Generalized Bilevel Programming Problems

VIEW 12 EXCERPTS

HIGHLY INFLUENTIAL

## THE NONLINEAR BILEVEL PROGRAMMING PROBLEM: FORMULATIONS, REGULARITY AND OPTIMALITY CONDITIONS

VIEW 11 EXCERPTS

HIGHLY INFLUENTIAL

## On the co-derivative of normal cone mappings to inequality systems ☆

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL