Lectures on Mathematical Theory of Extremum Problems

Editor’s preface -- Lecture 1. Introduction -- Lecture 2. Topological linear spaces, convex sets, weak topologies -- Lecture 3. Hahn-Banach Theorem -- Lecture 4. Supporting hyperplanes and extremal points -- Lecture 5. Cones, dual cones -- Lecture 6. Necessary extremum conditions (Euler-Lagrange equation) -- Lecture 7. Directions of decrease -- Lecture 8. Feasible directions -- Lecture 9. Tangent directions -- Lecture 10. Calculation of dual cones -- Lecture 11. Lagrange multipliers and the Kuhn-Tucker Theorem -- Lecture 12, Problem of optimal control. Local maximum principle -- Lecture 13. Problem of optimal control. Maximum principle -- Lecture 14. Problem of optimal control. Constraints on phase coordinates, minimax problem -- Lecture 15. Sufficient extremum conditions -- Lecture 16. Sufficient extremum conditions. Examples -- Suggestions for further reading -- References.