Читать книгу Multi-parametric Optimization and Control - Efstratios N. Pistikopoulos - Страница 27

If one step of the dual simplex algorithm consists of changing one element of the active set, i.e. let , then the dual pivot involving the constraint yields .

The first‐order constraint qualifications that will be presented in the following text are necessary prerequisites to identify whether a feasible point is a local optimum of the function .

 Linear independence constraint qualification: The gradients for all and for all are linearly independent.

 Slater constraint qualification: The constraints for all are pseudo‐convex1 at , while the constraints for all are quasi‐convex or quasi‐concave.2 In addition, the gradients are linearly independent and there exists such that and .