Optimality Conditions

In this chapter, we study optimality conditions for several mathematical programs involving type-I and other related functions.

EquationSource $$\begin{array}{l} x > y \, \textrm{if and only if} \, x_{i} > y_{i}, i = 1,2,\ldots, n,\\ x \geqq y \, \textrm{if and only if} \, x_{i} \geqq y_{i}, i = 1,2,\ldots, n,\\ x \geq y \, \textrm{if and only if} \, x_{i} \geqq y_{i}, i = 1,2,\ldots, n, \, \textrm{but} \, x \neq y. \end{array}$$