The concept of convexity has far-reaching consequences in variational analysis. In the study of maximization and minimization, the division between problems of convex or nonconvex type is as significant as the division in other areas of mathematics between problems of linear or nonlinear type. Furthermore, convexity can often be introduced or utilized in a local sense and in this way serves many theoretical purposes.


Line Segment Convex Function Convex Hull Convex Combination Piecewise Linear Function 
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© Springer-Verlag Berlin Heidelberg 1998

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