Linear and Convex Optimization. Michael H. Veatch

Linear and Convex Optimization

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11 Chapter 11Figure 11.1 Heavy lines are a spanning tree of the directed graph.Figure 11.2 A network flow problem for Figure 11.1.Figure 11.3 Three spanning tree solutions. The dotted line is an entering ar...Figure 11.4 An infeasible network flow problem.Figure 11.5 A transportation problem with three supply nodes and two demand ...Figure 11.6 Initial tree solution for Figure 11.5.Figure 11.7 Final tree solution for Figure 11.5.Figure 11.8 Progress of algorithm for Example 11.7.

12 Chapter 12Figure 12.1 Feasible region for Example 12.1.Figure 12.2 Feasible region and convex hull for Example 12.1.Figure 12.3 Renumbering a spanning tree. Node and arc numbers in parentheses...

13 Chapter 13Figure 13.1 A branch and bound tree.Figure 13.2 Branch and bound tree for Example 13.1 after the first branching...Figure 13.3 Branch and bound tree for Example 13.1.Figure 13.4 Branch and bound tree for Example 13.2.Figure 13.5 A cutting plane for

.Figure 13.6 Feasible region for Example 13.4. The dashed line is a C–G inequ...

14 Chapter 14Figure 14.1 Optimality condition with one constraint

.Figure 14.2 Optimality condition with one constraint

.Figure 14.3 Optimality condition with two inequality constraints.Figure 14.4 Points

and

satisfy the KKT conditions but are not local maxi...Figure 14.5 Primal and dual functions with a duality gap.Figure 14.6 Primal function with no duality gap.Figure 14.7 Primal function for Example 14.5 with no duality gap.

15 Chapter 15Figure 15.1 Problems with optimal solutions in the interior and on an edge....Figure 15.2 Gradient search.Figure 15.3 Moving to the interior point

or the boundary point