Elements of Convex Analysis. Linear Theorems of the Alternative. Tangent Cones

Giorgio Giorgi (), Bienvenido Jiménez () and Vicente Novo ()
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Giorgio Giorgi: University of Pavia
Bienvenido Jiménez: National University of Distance Education
Vicente Novo: National University of Distance Education

Chapter Chapter 2 in Basic Mathematical Programming Theory, 2023, pp 23-52 from Springer

Abstract: Abstract Mathematical programming theory is strictly connected with Convex Analysis. We give in the present section the main concepts and definitions regarding convex sets and convex cones. Convex functions and generalized convex functions will be discussed in the next chapter. Geometrically, a set $$S\subset \mathbb {R}^n$$ S ⊂ R n is convex Setconvexif the line segment joining any two points in the set lies entirely in the set. We recall that the (closed) line segment joining the points $$x^{1}$$ x 1 and $$x^{2}$$ x 2 of S, denoted as $$\left[ x^{1},x^{2}\right] $$ x 1 , x 2 .

Date: 2023
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DOI: 10.1007/978-3-031-30324-1_2

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