A Constant Rank Constraint Qualification in Continuous-Time Nonlinear Programming

A Constant Rank-type Constraint Qualification for Multi-Objective Continuous-Time Nonlinear Programming

“…In Monte and de Oliveira [6], KKT-type necessary optimality conditions were provided under a slightly different constant rank condition: the integer number r t in definition above were assumed to be constant with respect to t. Recently, we realized that, if the integer number r is allowed to vary with the parameter t ∈ [0, T ], then the results are still valid. With such changes, the following result is proved similarly to [6]. Proposition 3.1.…”

“…The optimality conditions were developed for efficient solutions, also known as Pareto solutions. A relaxed version of the constant rank-type constraint qualification given in Monte and de Oliveira [6] for the mono-objective case is used here for establishing the KKT-type conditions.…”

“…Some preliminaries are given in Section 2, where some important assumptions and the definition of efficient solutions are stated. In Section 3, a review of the scalar problem is performed, and a small (but important) adjustment is made to the results of Monte and de Oliveira [6]. In Section 4, Karush-Kuhn-Tucher necessary optimality conditions for continuous-time optimality problems are derived.…”

Second-Order Geometric Characterization of Optimal Solutions in Continuous-Time Programming

“…where f : R n × [0, T ] → R and g : R n × [0, T ] → R m . Second-order necessary optimality conditions for this kind of problems were derived just recently in the literature in Monte and de Oliveira [2,3]. In these papers, a more general problem, with equality and inequality constraints, is considered.…”

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

“…Besides convergence of algorithms and stability analysis, CRCQ was used in several contexts, such as NLP [4,13,46], MPEC [33], vector optimization [44], and continuous-time NLP [49], for studying necessary second-order optimality conditions. One of the main goals of this paper is to bring such results to more general conic programming contexts, namely nonlinear second-order cone programming (NSOCP) and nonlinear semidefinite programming (NSDP).…”