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Preface 1. Introduction Part I. Theory: 2. Convex sets 3. Convex functions 4. Convex optimization problems 5. Duality Part II. Applications: 6. Approximation and fitting 7. Statistical estimation 8. Geometrical problems Part III. Algorithms: 9. Unconstrained minimization 10. Equality constrained minimization 11. Interior-point methods Appendices.