Handling Constraints

Abstract

The general nonlinear programming problem NLP is to find x so as to optimize

$$optimizef(x),x = ({{x}_{1}}, \ldots ,{{x}_{q}}) \in {{R}^{q}},$$

subject to p ≥0 inequalities:

$${{g}_{i}}(x) = 0,j = 0, \ldots ,p,$$

and m−p ≥0 equations:

$${{h}_{j}}(x)0,j = p + 1, \ldots ,m.$$

A traveler in quest of the divine asked the Master how to distinguish a true teacher from a false one when he got back to his own land.

Said the Master, ‘A good teacher offers practice; a bad one offers theories.’

‘But how shall I know good practice from bad?’

‘In the same way that the farmer knows good cultivation from bad?’

Anthony de Mello, One Minute Wisdom