1. Introduction. - 2. The Mayer-Bolza Problem for Several Independent Variables: Necessary Conditions for a Minimum. - 3. Optimal Distribution of the Resistivity of the Working Medium in the Channel of a Magnetohydrodynamic Generator. - 4. Relaxation of Optimization Problems with Equations Containing the Operator ? ? ?: An Application to the Problem of Elastic Torsion. - 5. Relaxation of Some Problems in the Optimal Design of Plates. - 6. Optimal Control of Systems Described by Equations of Hyperbolic Type. - 7. Parabolic and Other Evolution Optimization Problems. - 8. Bellman's Method in Variational Problems with Partial Derivatives. - Appendix A: Calculations and Comments. - Appendix B: Remarks and Guide to the Literature. - References. Language: English