Convex optimization concave, and therefore a problem and then such problems are formulated in the standard form of convex optimization problems, that is, minimizing the convex objective function. For nonlinear convex minimization, the associated maximization problem obtained by substituting the supremum operator for the infimum operator is not a problem of convex optimization, as conventionally defined. However, it is studied in the larger field of convex optimization as a problem of convex maximization. The convex maximization problem is especially important for studying the existence of maxima. Consider the restriction of a convex function to a compact convex set: Then, on that set,
Lens (optics) object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of a lens of focal length "f" are focused at a point with distance from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped