Abstract
In the previous chapter, we study the minimization problem of a convex function under convex constraints. In this chapter, we study the minimization problem for two other classes of functions. The first ones are quasi-convex functions. We know (see Chapter 5) that for a convex function f, any level set of f is convex. But the converse is not true. The functions which have the property that every level set is convex are precisely called quasi-convex functions. In the first section we give necessary and sufficient conditions for a point to be a solution to a minimization problem of a quasi-convex function under convex constraints.
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