Level Sets and Continuity of Conjugate Convex Functions

Convex Sets and Convex Functions

In this section, we introduce one of the most important ideas in economic modelling, in the theory of optimization and, indeed in much of modern analysis and computatyional mathematics: that of a convex set. Almost every situation we will meet will depend on this geometric idea. As an independent idea, the notion of convexity appeared at the end of the 19 century, particularly in the works of M...

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

(Convex) Level Sets Integration

The paper addresses the problem of recovering a pseudoconvex function from the normal cones to its level sets that we call the convex level sets integration problem. An important application is the revealed preference problem. Our main result can be described as integrating a maximally cyclically pseudoconvex multivalued map that sends vectors or “bundles” of a Euclidean space to convex sets in...

some properties of certain subclasses of close-to-convex and quasi-convex functions with respect to 2k-symmetric conjugate points

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Analysis of Convex Sets and Functions