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Analyze first the convexity of the functions given.
Convex function: 2nd derivative posititve.
Concave function: 2nd derivative negative
Neither convex nor concave.
Convex function
Concave function
Linear function. Either convex or concave.
Analyze the objective and constraint functions for the nonlinear programming models.
Model
Found Global Optimum? Justify
The objective function is convex because a(x) is convex and -b(x) is convex.
The constraint is linear so the feasible region is a convex region.
The local minimum is the global minimum.
The objective function is linear, so it can be concave.
The first constraint defines a region that is not convex, so the feasible region is not convex.
Global optimum not necessarily found.
We have found the global minimum.
The objective function, d(x), is convex
a(x) - b(x) is convex, so the first constraint defines a convex region.
f(x) is linear and convex, so the second constraint defines a convex region.
e(x) is concave so - e(x) is convex.
The feasible region is convex, so the local minimum is the global minimum.
Operations Research Models and Methods Internet by Paul A. Jensen Copyright 2001 - All rights reserved
