Problem of improvement of objective function with indeterminate gradient (Q1086167)

The article considers the optimization problem in the case in which an explicit expression for the objective function is not known. Some point \(x^ 0\in X\) is chosen; it is assumed that experts can formulate a number of constraints for the gradient of the objective function at this point, in the form of linear homogeneous inequalities that define its cone of possible directions. Then the direction is determined along which, moving from point \(x^ 0\), the best guaranteed result is obtained under conditions of an indeterminate gradient of the objective function.