CONSTANT RANK CONSTRAINT QUALIFICATIONS: A GEOMETRIC INTRODUCTION
نویسندگان
چکیده
منابع مشابه
Constant rank constraint qualifications: a geometric introduction
Constraint qualifications (CQ) are assumptions on the algebraic description of the feasible set of an optimization problem that ensure that the KKT conditions hold at any local minimum. In this work we show that constraint qualifications based on the notion of constant rank can be understood as assumptions that ensure that the polar of the linear approximation of the tangent cone, generated by ...
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An example in which CRCQ holds. The left figure shows a set S(u) defined by 3 constraints. The normal cone NS(u)(x) is the cone generated by the two dashed halflines originated from the point x. The red curve indicates the neighborhood X. The normal cone NS(u)(x) has four nonempty faces, and the family {I(x′, u), x′ ∈ S(u)∩X} contains four elements {1, 3},{1},{3} and ∅, each of which correspond...
متن کاملConstraint Qualifications for Nonlinear Programming
This paper deals with optimality conditions to solve nonlinear programming problems. The classical Karush-Kuhn-Tucker (KKT) optimality conditions are demonstrated through a cone approach, using the well known Farkas’ Lemma. These conditions are valid at a minimizer of a nonlinear programming problem if a constraint qualification is satisfied. First we prove the KKT theorem supposing the equalit...
متن کاملConstant-Rank Condition and Second-Order Constraint Qualification
The constant-rank condition for feasible points of nonlinear programming problems was defined by Janin (Math. Program. Study 21:127–138, 1984). In that paper, the author proved that the constant-rank condition is a first-order constraint qualification. In this work, we prove that the constant-rank condition is also a secondorder constraint qualification. We define other second-order constraint ...
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This paper studies solution properties of a parametric variational condition under the constant rank constraint qualification (CRCQ), and properties of its underlying set. We start by showing that if the CRCQ holds at a point in a fixed set, then there exists a one-to-one correspondence between the collection of nonempty faces of the normal cone to the set at that point and the collection of ac...
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ژورنال
عنوان ژورنال: Pesquisa Operacional
سال: 2014
ISSN: 0101-7438
DOI: 10.1590/0101-7438.2014.034.03.0481