Convex analysisConvex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization, a subdomain of optimization theory. Convex set A subset of some vector space is if it satisfies any of the following equivalent conditions: If is real and then If is real and with then Convex function Throughout, will be a map valued in the extended real numbers with a domain that is a convex subset of some vector space.
Resource depletionResource depletion is the consumption of a resource faster than it can be replenished. Natural resources are commonly divided between renewable resources and non-renewable resources (see also mineral resource classification). Use of either of these forms of resources beyond their rate of replacement is considered to be resource depletion. The value of a resource is a direct result of its availability in nature and the cost of extracting the resource, the more a resource is depleted the more the value of the resource increases.
