Convex optimization linear programming. Many optimization problems can be reformulated as convex minimization problems. For example, the problem of "maximizing" a "concave function" formula_1 can be re-formulated equivalently as a problem of minimizing the convex function formula_2. An optimization problem, which aims to find a point formula_3 such that formula_4 for all formula_5 in some feasible set formula_6, is convex if and only if formula_6 and the objective function formula_1 satisfy the following two properties: Perhaps more conveniently, the convex problem can be phrased in the more shorthand general definition of optimization: finding some formula_19 such that for some feasible set formula_6
Crepuscular rays Crepuscular rays Crepuscular rays (more commonly known as sunbeams, sun rays, splintered light, or god rays), in atmospheric optics, are rays of sunlight that appear to radiate from the point in the sky where the Sun is located. Shining through openings in clouds (particularly stratocumulus) or between other objects, these columns of sunlit particulates are separated by darker cloud-shadowed volumes. Despite seeming to converge toward the light source, the rays are in fact near-parallel shafts of sunlight. Their apparent convergence is a perspective effect. This phenomenon mimics the way parallel railway lines or long hallways, for example, seem to seek