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Constrained Optimization: Kuhn-Tucker conditions

Constrained optimization : Kuhn-Tucker conditions Brian Wallace, Economics dept September 23, 2004. Abstract In this document, we set out the Constrained optimisation with inequality constraints and state the Kuhn-Tucker necessary conditions for a solution; after an example , we state the kuhn - tucker sufficient conditions for a maximum. 1 The Problem Suppose we have a function f , which we wish to maximise, together with some constraints, gi ci , which must be satisfied. This leads us to the problem: g1 (x) c1. g2 (x) c2.. max f (x) subject to . gm (x) cm xi 0. We have seen how to solve this problem with equality constraints; we introduce a number of mul- tipliers 1 ,.. , m and form the Lagrangian which we partially differentiate with respect to each xi and each j and set equal to 0, to get a system of m + n equations with nm variables.

Constrained Optimization: Kuhn-Tucker conditions Brian Wallace, Economics dept b.wallace@rhul.ac.uk September 23, 2004 Abstract In this document, we set out the constrained optimisation with inequality constraints and state the Kuhn-Tucker necessary conditions for a solution; after an example, we state the Kuhn-Tucker sufficient conditions for ...

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