Convex Optimization - Convex Optimization Problem

Convex Optimization Problem

An optimization problem (also referred to as a mathematical programming problem or minimization problem) of finding some such that

where is the feasible set and is the objective, is called convex if is a closed convex set and is convex on . Alternatively, an optimization problem on the form

\begin{align} &\operatorname{minimize}& & f(x) \\ &\operatorname{subject\;to} & &g_i(x) \leq 0, \quad i = 1,\dots,m \end{align}

is called convex if the functions are convex.

Read more about this topic:  Convex Optimization

Famous quotes containing the word problem:

    “The problem is simply this: no one can feel like CEO of his or her life in the presence of the people who toilet trained her and spanked him when he was naughty. We may have become Masters of the Universe, accustomed to giving life and taking it away, casually ordering people into battle or out of their jobs . . . and yet we may still dirty our diapers at the sound of our mommy’s whimper or our daddy’s growl.”
    —Frank Pittman (20th century)