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Unformatted text preview: i=1, 2, 3 Write the optimality conditions for the problem and use it to obtain the optimal solution. Justify your answer. Problem 4 Read each of the following statements carefully to see whether it is true or false . Justify your answers (no credit for answers without justification!) 1) If x* is a point satisfying the Karush-Kuhn-Tucker conditions for a maximization problem with a concave objective function over some inequality constrains then x* is a global maximum point. 2) If all leading principal minors of the Hessian of a function f : Rn→R are positive for all points in Rn, then f is a convex function. 3) For the following single variable nonlinear programming problem: Max f(x) s.t. g(x)=b, Let L(x,λ)=f(x)+λ(b-g(x)). If (x*,λ*) satisfies: ∂f/∂x=∂f/∂λ=0, then x* is an optimal solution....
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This note was uploaded on 02/17/2010 for the course IEOR 160 taught by Professor Hochbaum during the Fall '07 term at University of California, Berkeley.
- Fall '07
- Operations Research