Tent Method, optimization and robustness

The Tent Method solves different extremal problems (minima and maxima of smooth functions, minimax problems, optimization problems, etc.). A detailed description of the Method with its geometrical and topological foundations is given. The Tent Method has application to optimization problems; in particular, it allows to prove the Maximum Principle . The last section contains the sufficient condition of optimality (in a revised form) and the robust optimization problems . We show that the regular synthesis (which is the main instrument in the sufficient conditions of optimality) ensures the robustness. The text is illustrated by figures and examples. Copyright © 2004 John Wiley & Sons, Ltd.