Weekly Activities

Time: 9h00, Wednesday, October 2, 2019
Location: Rom 302, Building A5, Institute of Mathematics
Abstract: This paper presents two new theorems on Geoffrion's properly efficient solutions and a series of illustrative examples for linear fractional vector optimization problems with unbounded constraint sets. Provided that all components of objective function are properly fractional, the first theorem gives sufficient conditions for the efficient solution set to coincide with Geoffrion's properly efficient solution set. Admitting that the objective function can have  some affine components, in the second theorem we give sufficient conditions for an efficient solution to be a Geoffrion's properly efficient solution. The recession cone of the constraint set, the derivatives of the scalar objective functions, but no tangent cone to the constraint set at the efficient point, are used in the second theorem.