Special Nonconvex Optimization Problems Turnable into Problems of Linear Programming

Abstract

The present article is connected with the article “About a special class of nonconvex optimization problems” (Grygarova 1990). This article deals with such nonconvex optimization problems (NOPs), feasible sets of which are so-called spherical polyhedrons (a spherical polyhedron is the intersection of a polyhedral cone having a vertex at the origin point a with a hypersphere with the centre at a) and objective functions are special nonconvex continuous strictly monotone functions of a certain argument. In the article of Grygarova (1990) it was proved that such NOP is globally solvable and that its optimal solution set (the set of all optimal points) represents a closure of a face of the considered spherical polyhedron. On the basis of these results we can suppose that there exists a certain close connection between such NOPs and linear optimization problems. It appears that these NOPs can be transfer into equivalent linear optimization problems.