Convex optimization theory - Bertsekas, dimitri (Hyaderabad (India) Universities press (India) private LTD., 2010)
The book, Convex Optimization Theory provides an insightful, concise and rigorous treatment of the basic theory of convex sets and functions in finite dimensions and the analytical/geometrical foundations of convex optimization and duality theory. The convexity theory is developed first in a simple accessible manner using easily visualized proofs. The focus then shifts to a transparent geometrical line of analysis to develop the fundamental duality between descriptions of convex sets and functions in terms of points and in terms of hyperplanes.
Keywords: Mathematical optimization; Fonctions convexes; Convex functions