1.1 Optimization Problems.
1.2 Basic Mathematical Preliminaries and Notations.
References to Chapter I.
CHAPTER II.CONVEX SETS, CONVEX AND GENERALIZED CONVEX FUNCTIONS.
2.1 Convex Sets and Their Main Properties.
2.2 Separation Theorems.
2.3 Some Particular Convex Sets. Convex Cone.
2.4 Theorems of the Alternative for Linear Systems.
2.5 Convex Functions.
2.6 Directional Derivatives and Subgradients of Convex Functions.
2.7 Conjugate Functions.
2.8 Extrema of Convex Functions.
2.9 Systems of Convex Functions and Nonlinear Theorems of the Alternative.
2.10 Generalized Convex Functions.
2.11 Relationships Between the Various Classes of Generalized Convex Functions. Properties in Optimization Problems.
2.12 Generalized Monotonicity and Generalized Convexity.
2.13 Comparison Between Convex and Generalized Convex Functions.
2.14 Generalized Convexity at a Point.
2.15 Convexity, Pseudoconvexity and Quasiconvexity of Composite Functions.
2.16 Convexity, Pseudoconvexity and Quasiconvexity of Quadratic Functions.
2.17 Other Types of Generalized Convex Functions References to Chapter II.
CHAPTER III.SMOOTH OPTIMIZATION PROBLEMS
SADDLE POINT CONDITIONS.
3.2 Unconstrained Extremum Problems and Extremum
Problems with a Set Constraint.
3.3 Equality Constrained Extremum Problems.
3.4 Local Cone Approximations of Sets.
3.5 Necessary Optimality Conditions for Problem (P) where the Optimal Point is Interior to X.
3.6 Necessary Optimality Conditions for Problems (P e); and The