Non-convex optimization problem definition

  • What is non-convex set?

    A set that is not convex is called a non-convex set.
    A polygon that is not a convex polygon is sometimes called a concave polygon, and some sources more generally use the term concave set to mean a non-convex set, but most authorities prohibit this usage..

  • What is the difference between convex and non-convex?

    A polygon is convex if all the interior angles are less than 180 degrees.
    If one or more of the interior angles is more than 180 degrees the polygon is non-convex (or concave)..

A non-convex optimization problem is any problem where the objective or any of the constraints are non-convex, as pictured below. Such a problem may have multiple feasible regions and multiple locally optimal points within each region.

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