# 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…

## 43 Citations

Mathematical programs with equilibrium constraints: a sequential optimality condition, new constraint qualifications and algorithmic consequences

- Computer Science, MathematicsOptim. Methods Softw.
- 2021

This paper presents a new sequential optimality condition useful for the convergence analysis of several methods for solving mathematical programs with equilibrium constraints such as relaxations schemes, complementarity-penalty methods, and interior-relaxation methods and the weakest constraint qualification for M-stationarity associated with such sequential Optimality condition is presented.

Sequential optimality conditions for cardinality-constrained optimization problems with applications

- Computer ScienceComput. Optim. Appl.
- 2021

This work derives a problem-tailored sequential optimality condition, which is satis ed at every local minimizer without requiring any constraint quali cation, and shows that, under a suitable KurdykaŁojasiewicz-type assumption, any limit point of a standard multiplier penalty method applied directly to the reformulated problem also satis es the optimality conditions.

On constraint qualifications for second-order optimality conditions depending on a single Lagrange multiplier

- Computer ScienceOper. Res. Lett.
- 2021

New constraint qualifications to ensure the validity of some well-known second-order optimality conditions that can be associated with numerical methods for solving constrained optimization problems are presented and discussed.

A sequential optimality condition for Mathematical Programs with Cardinality Constraints

- Computer Science, Mathematics
- 2020

An Approximate Weak stationarity ($AW$-stationarity) concept designed to deal with MPCaC (MPCaC) is proposed, and it is proved that it is a legitimate optimality condition independently of any constraint qualification.

A Guided Tour in Constraint Qualifications for Nonlinear Programming under Differentiability Assumptions

- Computer Science
- 2018

An up-to-date overview of several constraint quali?cations proposed in the literature for a nonlinear programming problem, under differentiability assumptions, and point out the various implications existing among the constraint qualifications considered.

Necessary optimality conditions and exact penalization for non-Lipschitz nonlinear programs

- Computer Science, MathematicsMath. Program.
- 2018

When the objective function is not locally Lipschitz, constraint qualifications are no longer sufficient for Karush–Kuhn–Tucker (KKT) conditions to hold at a local minimizer, let alone ensuring an…

Constraint Qualifications for Karush-Kuhn-Tucker Conditions in Constrained Multiobjective Optimization

- 2020

The notion of a normal cone of a given set is paramount in optimization and variational analysis. In this work, we give a definition of a multiobjective normal cone which is suitable for studying…

On AKKT optimality conditions for cone-constrained vector optimization problems

- Mathematics
- 2019

In this paper, we introduce a kind of approximate Karush--Kuhn--Tucker condition (AKKT) for a smooth cone-constrained vector optimization problem. We show that, without any constraint qualification,…

On the convergence of augmented Lagrangian strategies for nonlinear programming

- Mathematics
- 2021

Augmented Lagrangian algorithms are very popular and successful methods for solving constrained optimization problems. Recently, the global convergence analysis of these methods have been…

Sequential constant rank constraint qualifications for nonlinear semidefinite programming with applications

- Mathematics
- 2021

We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from nonlinear programming. As an application of these…

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