kuhn-tucker conditions – Optimization Online

A short derivation of the Kuhn-Tucker conditions

Published: 2011/05/17, Updated: 2011/05/19

Constrained Nonlinear Optimization economics, farkas's lemma, kuhn-tucker conditions, the method of lagrange multipliers

The Kuhn-Tucker conditions have been used to derive many significant results in economics. However, thus far, their derivation has been a little bit troublesome. The author directly derives the Kuhn-Tucker conditions by applying a corollary of Farkas’s lemma under the Mangasarian-Fromovitz constraint qualification. CitationDiscussion Paper Series A, No. 2011-234, Graduate School of Economics and Business … Read more

Transposition theorems and qualification-free optimality conditions

Published: 2005/05/11, Updated: 2006/02/20

Arnold Neumaier

Hermann Schichl

Constrained Nonlinear Optimization, Global Optimization Theory, Multi-Criteria Optimization certificate of global optimality, first order optimality conditions, fritz john conditions, global optimality condition, global optimization, karush-john conditions, kuhn-tucker conditions, mangasarian-fromovitz constraint qualification, necessary and sufficient conditions, positivstellensatz, second order optimality conditions, theorem of the alternative, transposition theorem

New theorems of the alternative for polynomial constraints (based on the Positivstellensatz from real algebraic geometry) and for linear constraints (generalizing the transposition theorems of Motzkin and Tucker) are proved. Based on these, two Karush-John optimality conditions — holding without any constraint qualification — are proved for single- or multi-objective constrained optimization problems. The first … Read more