A METHOD FOR SOLVING NONLINEAR MAXIMUM-PROBLEMS DEPENDING ON PARAMETERS.
Research rept., No. 79.
CARNEGIE INST OF TECH PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP
Pagination or Media Count:
Parametric maximum problems are treated with the aim of representing an optimal solution explicitly as a function of the parameter. The method developed for this purpose permits one to divide the given parameter interval uniquely into a finite number of subintervals in a manner that makes it possible to attach to each of them a system of equations which depends upon the parameter in such a way that the solution of these equations corresponds to the optimal solution. These systems of equations are linear for maximum problems with quadratic objective function and linear restraints. Their solutions give the components of the optimal solution in the form of quotients of polynomials of the parameter and a further extension of this method comprehends the solution of quadratic maximum problems with strictly concave objective function and linear restraints. Author
- Theoretical Mathematics