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February 9th, 2017, 11:17 PM  #1 
Newbie Joined: Feb 2017 From: lebanon Posts: 1 Thanks: 0  Is ln(1+x/(by+a)) concave function? (x,y,a and b are positive real numbers)
From boyd's book: the composition of a concave function with affine function is a concave function. As we can see ln(x) is concave function and g(x,y)=x/(by+a) is linearfractional function so ln(1+x/(by+a)) should be concave function. On the other hand, the hessian matrix of a concave function must be negative semidefinite which is not the case for this function. So in your opinion, is ln(1+x/(by+a)) concave function or not. If not can we consider it as quasiconcave function so we can use the Lagrangian method to solve such optimization problem. 
February 10th, 2017, 01:38 AM  #2  
Senior Member Joined: Sep 2016 From: USA Posts: 609 Thanks: 378 Math Focus: Dynamical systems, analytic function theory, numerics  Quote:
 

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concave, convex optimization, function, ln1, numbers, positive, real, x or by 
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