The theory of convex sets is a vibrant and classical field of modern mathe matics with rich applications in economics and optimization the material in these notes is introductory starting with a small chapter. Lectures on convex sets is self contained and unified in presentation the book grew up out of various courses on geometry and convexity taught by the author for more than a decade the book grew up out of various courses on geometry and convexity taught by the author for more than a decade. Lectures on convex sets valeriu soltan on amazoncom free shipping on qualifying offers the book is carefully written and should be useful as a textbook for courses on convex geometry reviews clippings this is an extremely complete book on the fundamentals of the algebraic and topological properties of convex sets this is a . Convex analysis is of extreme importance in mathematics especially in optimization fortunately there are numerous excellent books on this subject this new one is equally outstanding soltans text has detailed coverage of the algebraic and geometric properties of subspaces affine sets convex sets and cones. Images and inverse images of convex sets under linear fractional functions are convex convex sets 2 14 example of a linear fractional function fx 1 x1 x2 1 x x1 x 2 c 1 0 1 1 0 1 x1 x 2 fc 1 0 1 1 0 1 convex sets 2 15 generalized inequalities a convex cone k rn is a proper cone if