karush-john conditions – Optimization Online

Transposition theorems and qualification-free optimality conditions

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

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