Optimality conditions and constraint qualifications for cardinality constrained optimization problems

Strict Constraint Qualifications and Sequential Optimality Conditions for Constrained Optimization

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 strict constraint qualification associated with some sequential optimality c...

Constraint qualifications and optimality conditions for optimization problems with cardinality constraints

This paper considers optimization problems with cardinality constraints. Based on a recently introduced reformulation of this problem as a nonlinear program with continuous variables, we first define some problem-tailored constraint qualifications and then show how these constraint qualifications can be used to obtain suitable optimality conditions for cardinality constrained problems. Here, th...

Necessary optimality conditions for constrained optimization problems under relaxed constraint qualifications

We derive firstand second-order necessary optimality conditions for set-constrained optimization problems under the constraint qualificationtype conditions significantly weaker than Robinson’s constraint qualification. Our development relies on the so-called 2-regularity concept, and unifies and extends the previous studies based on this concept. Specifically, in our setting constraints are giv...

Constraint Qualifications and Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints

A very general optimization problem with a variational inequality constraint, inequality constraints, and an abstract constraint are studied. Fritz John type and Kuhn–Tucker type necessary optimality conditions involving Mordukhovich coderivatives are derived. Several constraint qualifications for the Kuhn–Tucker type necessary optimality conditions involving Mordukhovich coderivatives are intr...

Optimality Conditions for Constrained Optimization Problems