Naive constant rank-type constraint qualifications for multifold second-order cone programming and semidefinite programming

Sequential constant rank constraint qualifications for nonlinear semidefinite programming with applications

“…where f : R n → R and G : R n → S m are continuously differentiable functions, and is the partial order induced by S m + ; that is, M N if, and only if, M − N ∈ S m + . Equality constraints are omitted in (NSDP) for simplicity of notation, but our definitions and results are flexible regarding inclusion of such constraints, which should be done in the same way as in [7]. Moreover, throughout the whole paper, we will denote the feasible set of (NSDP) by F.…”

“…The first extension of CRCQ to nonlinear second-order cone programming (NSOCP) appeared in [32], but it was shown to be incorrect in [2]. A second proposal [7], which encompasses also nonlinear semidefinite programming (NSDP) problems, consists of transforming some of the conic constraints into NLP constraints via a reduction function, whenever it was possible, and then demanding constant linear dependence of the reduced constraints, locally. This was considered by the authors a naive extension, since it basically avoids the main difficulties that are expected from a conic framework.…”

First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition

“…This event has motivated us to investigate other possible extensions of CRCQ to conic problems, and their properties. The first step in this direction was made in [6], for NSOCP and NSDP problems with multiple constraints. The idea of [6] is to rewrite some of the conic constraints as locally equivalent NLP constraints, whenever possible, and then jointly applying nondegeneracy and the NLP version of CRCQ to the resulting problem.…”

“…The first step in this direction was made in [6], for NSOCP and NSDP problems with multiple constraints. The idea of [6] is to rewrite some of the conic constraints as locally equivalent NLP constraints, whenever possible, and then jointly applying nondegeneracy and the NLP version of CRCQ to the resulting problem. Later, in [8], based on the ideas from [7], we improved this strategy by exploiting the eigenvector structure of the semidefinite cone to deal with the conic constraints that could not be rewritten as NLP constraints.…”

Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators

“…Sequential optimality conditions have played a vital role in unifying and extending global convergence results for several classes of algorithms for general nonlinear optimization, Andreani et al [46] extended these concepts for nonlinear semidefinite programming. Andreani et al [47] discussed simple extensions of constant rank-type constraint qualifications to semidefinite programming, which are based on the Approximate Karush-Kuhn-Tucker necessary optimality condition and on the application of the reduction approach.…”