Properties of Convex and Concave Functions

Convex functions can be combined in a number of ways to produce new convex functions as illustrated by the following  

Remark 1 The epigraph of a convex function and the hypograph of a concave function are convex sets. 

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This section presents (i) the definitions and properties of convex and concave functions, (ii) the definitions of continuity, semicontinuity and subgradients, (iii) the definitions and properties of differentiable convex and concave functions, and (iv) the definitions and properties of local and global extremum points. 

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