Search results
Results from the WOW.Com Content Network
The policy is characterized by two numbers s and S, , such that when the inventory level falls below level s, an order is issued for a quantity that brings the inventory up to level S, and nothing is ordered otherwise. Gallego and Sethi [2] have generalized the concept of K-convexity to higher dimensional Euclidean spaces.
The concept of strong convexity extends and parametrizes the notion of strict convexity. Intuitively, a strongly-convex function is a function that grows as fast as a quadratic function. [11] A strongly convex function is also strictly convex, but not vice versa.
Modeling tools are separate pieces of software that let the user specify an optimization in higher-level syntax. They manage all transformations to and from the user's high-level model and the solver's input/output format. The table below shows a mix of modeling tools (such as CVXPY and Convex.jl) and solvers (such as CVXOPT and MOSEK).
In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates (duration is the first derivative). In general, the higher the duration, the more sensitive the bond price is to the change in ...
Let : be a convex function with domain . A classical subgradient method iterates (+) = () where () denotes any subgradient of at (), and () is the iterate of . If is differentiable, then its only subgradient is the gradient vector itself.
This difference in convexity can also be used to explain the price differential from an MBS to a Treasury bond. However, the OAS figure is usually preferred. The discussion of the "negative convexity" and "option cost" of a bond is essentially a discussion of a single MBS feature (rate-dependent cash flows) measured in different ways.
The concept of K-convexity generalizes K-convexity introduced by Scarf (1960) [2] to higher dimensional spaces and is useful in multiproduct inventory problems with fixed setup costs. Scarf used K-convexity to prove the optimality of the (s, S) policy in the single product case. Several papers are devoted to obtaining optimal policies for ...
then is called strictly convex. [1]Convex functions are related to convex sets. Specifically, the function is convex if and only if its epigraph. A function (in black) is convex if and only if its epigraph, which is the region above its graph (in green), is a convex set.