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Lecture 2 - Chapter11 LECTURE 2 Reference W L Winston...

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1 Chapter 11 Nonlinear Programming LECTURE 2 Reference: W. L. Winston, Operations Research: Applications and Algorithms , 4th Edition, Brooks/Cole, Thomson Learning, 2004 .
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2 Local Extremum For any NLP (maximization), a feasible point   x  = ( x 1 , x 2 ,…, x n ) is a local maximum  if for sufficiently small  , any feasible point                 x’  =  ( x’ 1 , x’ 2 ,…, x’ n ) having |  x i x’ i |<  ( = 1,2,…, n ) satisfies  f(x) f ( x ’). A point that is  a local maximum or a local minimum is called a local, or relative extremum.  For an LP (max prob) any local maximum is an optimal solution to the LP.  For a general NLP this may not  be true.  10 0 . . ) ( max = x t s x f z A,B,C local maxima C unique optimal
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3 Proportionality and Additivity Assumptions Unlike an LP, an NLP may not  satisfy the Proportionality  and Additivity Assumptions. For ex:  Increasing L by 1 will increase z by K. The effect on z of  increasing L by 1 depends on K . (does not satisfy  additivity assump.) (z=KL) The ex. below does not satisfy the proportionality assump.  because doubling the value of x does not double the  contribution of x to the obj func.  0 , 1 . .
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