3.2. The Capital Budgeting Problem {Problem
H)
73
Weak Convergence
For each problem j in the set P*, either x
(
*° is infeasible for j or else
Stronger Convergence
For each problem j in the set Pk and each feasible solution χ to problem
Of course, conditions C and C are not sufficient to guarantee that repeated
partioning of the set Ρ will yield an optimal solution to Problem 0 with a
finite amount of computation, but for reasonably sized problems and large
digital computers the lack of a guarantee does not prove to be much of a
handicap.
Figure 3.2 assists in the interpretation of the branch and bound procedure outlined above. Figure 3.2 represents a tree. Each node of the tree
corresponds to a problem j.
/(i)(x<*>) (C)
k, either χ is nonfeasible for problem j ovf
U)
(x) < f
(k)
(x).
(C)
Fig. 3,2 Tree representation of the branch and bound procedure. The final nodes
represent single solutions.
H)
73
Weak Convergence
For each problem j in the set P*, either x
(
*° is infeasible for j or else
Stronger Convergence
For each problem j in the set Pk and each feasible solution χ to problem
Of course, conditions C and C are not sufficient to guarantee that repeated
partioning of the set Ρ will yield an optimal solution to Problem 0 with a
finite amount of computation, but for reasonably sized problems and large
digital computers the lack of a guarantee does not prove to be much of a
handicap.
Figure 3.2 assists in the interpretation of the branch and bound procedure outlined above. Figure 3.2 represents a tree. Each node of the tree
corresponds to a problem j.
/(i)(x<*>) (C)
k, either χ is nonfeasible for problem j ovf
U)
(x) < f
(k)
(x).
(C)
Fig. 3,2 Tree representation of the branch and bound procedure. The final nodes
represent single solutions.