
Chapter 3
Barrier-Function and
Penalty-Function Methods
3.1 Barrier Functions ................................................ 35
3.2 Examples of Barrier Functions ................................... 36
3.2.1 The Logarithmic Barrier Function ...................... 36
3.2.2 The Inverse Barrier Function ............................ 36
3.3 Penalty Functions ................................................ 39
3.4 Examples of Penalty Functions .................................. 39
3.4.1 The Absolute-Value Penalty Function .................. 39
3.4.2 The Courant-Beltrami Penalty Function ................ 40
3.4.3 The Quadratic-Loss Penalty Function .................. ...