Engineering Optimization: Theory and Practice, Fourth Edition

7.20 Augmented Lagrange Multiplier Method 461

whereX(k)denotes the starting vector used in the minimization ofA.The value ofrk
is updated as

rk+ 1 = crk, c> 1 (7.247)

The functionAis then minimized with respect toXto findX∗ k(+^1 )and the iterative
process is continued until convergence is achieved forλ(k)j orX∗. If the value ofrk+ 1
exceeds a prespecified maximum valuermax, it is set equal tormax. The iterative process
is indicated as a flow diagram in Fig. 7.20.

Figure 7.20 Flowchart of augmented Lagrange multiplier method.