Contents -- Preface -- Introduction -- Chapter 1 Preliminary Results on Functional Analysis -- 1.1 Preliminary notions and results -- 1.2 Closedness and interiority notions -- 1.3 Open mapping theorems -- 1.4 Variational principles -- 1.5 Exercises -- 1.6 Bibliographical notes -- Chapter 2 Convex Analysis in Locally Convex Spaces -- 2.1 Convex functions -- 2.2 Semi-continuity of convex functions -- 2.3 Conjugate functions -- 2.4 The subdifferential of a convex function -- 2.5 The general problem of convex programming -- 2.6 Perturbed problems -- 2.7 The fundamental duality formula -- 2.8 Formulas for conjugates and e-subdifferentials duality relations and optimality conditions -- 2.9 Convex optimization with constraints -- 2.10 A minimax theorem -- 2.11 Exercises -- 2.12 Bibliographical notes -- Chapter 3 Some Results and Applications of Convex Analysis in Normed Spaces -- 3.1 Further fundamental results in convex analysis -- 3.2 Convexity and monotonicity of subdifferentials -- 3.3 Some classes of functions of a real variable and differentiability of convex functions -- 3.4 Well conditioned functions -- 3.5 Uniformly convex and uniformly smooth convex functions -- 3.6 Uniformly convex and uniformly smooth convex functions on bounded sets -- 3.7 Applications to the geometry of normed spaces -- 3.8 Applications to the best approximation problem -- 3.9 Characterizations of convexity in terms of smoothness -- 3.10 Weak sharp minima well-behaved functions and global error bounds for convex inequalities -- 3.11 Monotone multifunctions -- 3.12 Exercises -- 3.13 Bibliographical notes -- Exercises - Solutions -- Bibliography -- Index -- Symbols and Notations.