Non-existence of the Algorithm that can Obtain the Optimal Solution for a Few Given Options of Investment in Constructive Mathematics

Constructive mathematics is simply a mathematical process of computational procedures. Constructive Mathematical Analysis is the contrast of the classical analysis. In this paper, I apply constructive mathematical analysis to prove that there could not be an algorithm that always chooses the optimal investment from a few given options in constructive mathematical economics. One of the main tools is the existence of partially defined unextendible algorithms.