Convex optimization result

  • What is the benefit of convex function?

    Convex functions play an important role in many areas of mathematics.
    They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties.
    For instance, a strictly convex function on an open set has no more than one minimum..

In a convex optimization problem, the feasible region -- the intersection of convex constraint functions -- is a convex region, as pictured below. With a convex objective and a convex feasible region, there can be only one optimal solution, which is globally optimal.

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