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,
Focal cloud Focal cloud A focal cloud is the collection of focal points of an "imperfect" lens or parabolic reflector whether optical, electrostatic or electromagnetic. This includes parabolic antennas and lens-type reflective antennas of all kinds. The effect is analogous to the circle of confusion in photography. In a perfect lens or parabolic reflector, rays parallel to the device's axis striking the lens or reflector all pass through a single point, the focal point. In an imperfectly constructed lens or reflector, rays passing through different parts of the element do not converge to a single point but have different focal points. The