Convex optimization of optimization problem is convex. "Standard form" is the usual and perhaps most intuitive form of describing a convex minimization problem. It consists of the following three parts: A convex minimization problem in standard form is thus written as In reality, this form of problem is exactly equivalent to a problem constrained by only equalities. You can rephrase the problem without equality constraints by replacing each equality constraint formula_52 with a pair of inequality constraints formula_64 and formula_65, and the previous analysis holds. This fact is why formula_53 being both convex and concave, i.e. both formula_53 and formula_68 are convex,
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