ANALYSIS OF OBJECTIVE SPACE IN MULTIPLE OBJECTIVE OPTIMIZATION (LINEAR PROGRAM, DUALITY, HYPERPLANE)

The multiple objective linear program (MOLP) will be considered as: maximize Cx subject to x (ELEM) X (INTERSECT) K where C (ELEM) B(U,Z) (i.e. C is a bounded linear operator from a topological linear space U to a topological linear space Z), X = x (ELEM) U: Ax = b, A (ELEM) B(U,V), V a topological linear space and K is the given ordering cone in U. x (ELEM) X (INTERSECT) K is efficient (optimal) and y = Cx is nondominated if there does not exist a x' (ELEM) X (INTERSECT) K such that y' = Cx' with y' - y (ELEM) P (i.e. y' (GREATERTHEQ) y) and y' (NOT=) y, where P is the given ordering cone in Z.;In Chapter 1 we present an application of MOLP which will motivate the objective space analysis. The theory of objective space analysis in finite dimensions is discussed in Chapter 2. In Chapter 3 we consider the MOLP in topological linear spaces. A necessary and sufficient condition for efficiency is derived. Also a duality theorem is given. Objective space analysis was first studied by J. P. Dauer. In Chapter 4 we generalize Dauer's result to topological linear spaces.