KANTOROVICH SPACES AND OPTIMIZATION

摘要

Subdifferential calculus is a branch of functional analysis whose main source is the theory of extremal problems. Consider an abstract minimization problem: x ∈ X, f(x) → inf. Here X is a vector space and f : X → R is a numeric function with possibly infinite values. We are usually interested in the quantity inf f(x), the value of the problem, and in a solution, or optimum plan; i.e., a point x satisfying f(x) = inf f(X). It is a rare occurrence to solve an arbitrary extremal problem explicitly, i.e., to exhibit the value of the problem and one of the solutions. As a rule, we must simplify the initial problem by reducing it using the details of the objective function.