Many engineering optimization problems can be cast as a Linear Program (LP). Linear Programming is an optimization problem where the objective function and the constraints are linear functions of the optimization variables. In addition, several nonlinear optimization problems can be solved by iteratively solving linearized versions of the original problem. This chapter focuses on the solution of Linear Programs. Different statements of the LP problem are introduced. The Simplex method is explained in both the tabular and matrix forms. Several approaches to the Simplex method are discussed.

Chapter Contents:

• 2.1 Introduction
• 2.2 Examples of linear programs
• 2.2.1 A farming example
• 2.2.2 A production example
• 2.2.3 Power generation example
• 2.2.4 Wireless communication example
• 2.2.5 A battery charging example
• 2.3 Standard form of an LP
• 2.4 Optimality conditions
• 2.5 The matrix form
• 2.6 Canonical augmented form
• 2.7 Moving from one basic feasible solution to another
• 2.8 Cost reduction
• 2.9 The classical Simplex method
• 2.10 Starting the Simplex method
• 2.10.1 Endless pivoting
• 2.10.2 The big M approach
• 2.10.3 The two-phase Simplex
• 2.11 Advanced topics
• A2.1 Minimax optimization
• A2.1.1 Minimax problem definition
• A2.1.2 Minimax solution using linear programming
• A2.1.3 A microwave filter example
• A2.1.4 The design of coupled microcavities optical filter
• References
• Problems

Inspec keywords: nonlinear programming; linear programming

Other keywords: Simplex method; LP problem; linear programming; nonlinear optimization problem

Subjects: Optimisation techniques; Optimisation; Optimisation techniques