Ademir Carlos Ribeiro Filho - Academia.edu (original) (raw)

Ademir Carlos Ribeiro Filho

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Papers by Ademir Carlos Ribeiro Filho

Research paper thumbnail of Karush-Kuhn-Tucker Optimality Conditions and Constraint Qualifications trhough a Cone Approach

Synergismus scyentifica …, 2009

This paper deals with optimality conditions to solve nonlinear programming problems. The classica... more This paper deals with optimality conditions to solve nonlinear programming problems. The classical Karush-Kuhn-Tucker (KKT) 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 equality between the polar of the tangent cone and the polar of the first order feasible variations cone. Although this condition is the weakest assumption, it is extremely difficult to be verified. Therefore, other constraints qualifications, which are easier to be verified, are discussed, as: Slater's, linear independence of gradients, Mangasarian-Fromovitz's and quasiregularity.

Research paper thumbnail of Karush-Kuhn-Tucker Optimality Conditions and Constraint Qualifications trhough a Cone Approach

Synergismus scyentifica …, 2009

This paper deals with optimality conditions to solve nonlinear programming problems. The classica... more This paper deals with optimality conditions to solve nonlinear programming problems. The classical Karush-Kuhn-Tucker (KKT) 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 equality between the polar of the tangent cone and the polar of the first order feasible variations cone. Although this condition is the weakest assumption, it is extremely difficult to be verified. Therefore, other constraints qualifications, which are easier to be verified, are discussed, as: Slater's, linear independence of gradients, Mangasarian-Fromovitz's and quasiregularity.

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