Summary: The aim of this paper is to study the class of maximization problems having linear constraints and an objective function given by the product of an affine function raised to a certain power and another affine function. For such a class of problems, several theoretical aspects are investigated: values of the exponent for which there exists a finite optimum for any feasible region, conditions implying a finite supremum, conditions which ensure that a local maximum is a global maximum, optimality conditions with respect to a vertex of the feasible region, and so on. The obtained results allow us to suggest, for any exponent, a sequential simplex-like method converging to a global optimal solution in a finite number of steps. This algorithm reduces to the one given by the author and L. Martein [Methods Oper. Res. 53, 33-44 (1986; Zbl 0694.90126)] for the linear fractional case.
For the entire collection see [Zbl 0788.00061].