Convex optimization descent, and nonsmooth filter methods. Solving even close-to-convex but non-convex problems can be computationally intractable. Minimizing a unimodal function is intractable, regardless of the smoothness of the function, according to results of Ivanov. Conventionally, the definition of the convex optimization problem (we recall) requires that the objective function "f" to be "minimized" and the feasible set be convex. In the special case of linear programming (LP), the objective function is both concave and convex, and so LP can also consider the problem of maximizing an objective function without confusion. However, for most convex minimization problems, the objective function is not
Compound refractive lens the order of meters, by using many lenses in series. To minimize the absorption the lens must be made from a material such as aluminium, beryllium, or lithium. CRLs were first demonstrated in the mid-1990s by a group of scientists at the ESRF. They drilled holes in an aluminium block, and achieved focusing in two dimensions. For X-rays a concave lens focuses the X-rays because the index of refraction is slightly below unity. In a CRL of this type the walls between the cylindrical holes act as concave lenses for X-rays traveling perpendicular to the axis of the drilled cylinders.