Optimization and robustness

Abstract

Using the sufficient condition of optimality recently obtained by the author [Boltyanski, V.G., 2001, Sufficient conditions for Lagrange, Mayer, and Bolza optimization problems. Mathematical Problems in Engineering, 7, 177–203.], we formulate a new conception of the robustness and formulate a sufficient condition of robustness. At the end of the article we recall another conception of robustness earlier formulated by Prof. A. Poznyak and the author [Boltyanski, V. and Poznyak, A., 1999, Robust maximum principle in minimax control. International Journal of Control, 72(4), 305–314; Boltyanski, V. and Poznyak, A., 1999, Robust maximum principle for minimax Bolza problem with terminal set. In: Proc. 14-th World Congress IFAC, Beijing, China, pp. 263–268; Boltyanski, V. and Poznyak, A., 2002, Linear multi-model time-optimization. Optimal control, Applications and Methods, Vol. 23 (Chichester: John Wiley & Sons, Ltd), pp. 141–161; Boltyanski, V.G. and Poznyak, A.S., 2002, Robust maximum principle for a measure space as uncertainty set. Dynamic Systems and Applications, Dynamic Publishers. Inc., 11 (2), 277–292.]. Some examples illustrate the text.

Keywords:

• Optimization
• Variational calculus
• Maximum principle
• Robustness
• Mathematics Subject Classifications: Primary 15A15
• 52A20
• Secondary 15A18
• 52B12

Notes

Dedicated to V.F. Demyanov on the occassion of his 65th birthday.

Additional information

Notes on contributors

V. Boltyanski

Dedicated to V.F. Demyanov on the occassion of his 65th birthday.