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Название: Convex Functions and Their Applications. A Contemporary Approach
Авторы: Niculescu C., Persson L.
Convexity is a simple and natural notion which can be traced back to
Archimedes (circa 250 B.C.), in connection with his famous estimate of the
value of π (by using inscribed and circumscribed regular polygons). He noticed
the important fact that the perimeter of a convex figure is smaller than
the perimeter of any other convex figure surrounding it.
As a matter of fact, we experience convexity all the time and in many
ways. The most prosaic example is our upright position, which is secured as
long as the vertical projection of our center of gravity lies inside the convex
envelope of our feet. Also, convexity has a great impact on our everyday life
through numerous applications in industry, business, medicine, and art. So
do the problems of optimum allocation of resources and equilibrium of noncooperative