Strict Constraint Qualifications and Sequential Optimality Conditions for Constrained Optimization

@article{Andreani2018StrictCQ,
  title={Strict Constraint Qualifications and Sequential Optimality Conditions for Constrained Optimization},
  author={Roberto Andreani and Jos{\'e} Mario Mart{\'i}nez and Alberto Ramos and Paulo J. S. Silva},
  journal={Math. Oper. Res.},
  year={2018},
  volume={43},
  pages={693-717}
}
Sequential optimality conditions for constrained optimization are necessarily satisfied by local minimizers, independently of the fulfillment of constraint qualifications. These conditions support the employment of different stopping criteria for practical optimization algorithms. On the other hand, when an appropriate property on the constraints holds at a point that satisfies a sequential optimality condition, such a point also satisfies the Karush-Kuhn-Tucker conditions. Those properties… 
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References

SHOWING 1-10 OF 44 REFERENCES
A Cone-Continuity Constraint Qualification and Algorithmic Consequences
TLDR
A cone-continuity property (CCP) is defined that will be shown to be the weakest possible constraint qualification (SCQ) and its relation to other constraint qualifications will be clarified.
On the behaviour of constrained optimization methods when Lagrange multipliers do not exist
TLDR
It will be shown that a straightforward version of the Newton–Lagrange (sequential quadratic programming) method fails to generate iterates for which a sequential optimality condition is satisfied, and a Newtonian penalty–barrier Lagrangian method guarantees that the appropriate stopping criterion eventually holds.
The Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints
Optimality criteria form the foundations of mathematical programming both theoretically and computationally. In general, these criteria can be classified as either necessary or sufficient. Of course,
A New Sequential Optimality Condition for Constrained Optimization and Algorithmic Consequences
TLDR
It is proved that a well-established augmented Lagrangian algorithm produces sequences whose limits satisfy the new condition of this type, and practical consequences are discussed.
A Practical Optimality Condition Without Constraint Qualifications for Nonlinear Programming
A new optimality condition for minimization with general constraints is introduced. Unlike the KKT conditions, the new condition is satisfied by local minimizers of nonlinear programming problems,
On Approximate KKT Condition and its Extension to Continuous Variational Inequalities
TLDR
This work introduces a necessary sequential Approximate-Karush-Kuhn-Tucker condition for a point to be a solution of a continuous variational inequality, and it is proved that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization.
A NECESSARY AND SUFFICIENT QUALIFICATION FOR CONSTRAINED OPTIMIZATION
A weak qualification is given which insures that a broad class of constrained optimization problems satisfies the analogue of the Kuhn–Tucker conditions at optimality. The qualification is shown to
A relaxed constant positive linear dependence constraint qualification and applications
TLDR
This work introduces a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that it is shown is enough to ensure the convergence of an augmented Lagrangian algorithm and that it asserts the validity of an error bound.
Pseudonormality and a Lagrange Multiplier Theory for Constrained Optimization
TLDR
Two new properties, pseudonormality and quasinormality, emerge as central within the taxonomy of interesting constraint characteristics and provide the connecting link between the classical constraint qualifications and two distinct pathways to the existence of Lagrange multipliers.
Interior-point ℓ2-penalty methods for nonlinear programming with strong global convergence properties
TLDR
Two line search primal-dual interior-point methods for nonlinear programming that approximately solve a sequence of equality constrained barrier subproblems and have strong global convergence properties under standard assumptions are proposed.
...
1
2
3
4
5
...