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CONVEX ANALYSIS. Convex Sets. Convex Functions and Generalizations. OPTIMALITY CONDITIONS AND DUALITY. The Fritz John and the Karush-Kuhn-Tucker Optimality Conditions. Constraint Qualifications. Lagrangian Duality and Saddle Point Optimality Conditions. ALGORITHMS AND THEIR CONVERGENCE. The Concept of an Algorithm. Unconstrained Optimization. Penalty and Barrier Functions. Methods of Feasible Directions. Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programming. Appendices. Bibliography. Index.