Normed vector spaceIn mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If is a vector space over , where is a field equal to or to , then a norm on is a map , typically denoted by , satisfying the following four axioms: Non-negativity: for every ,. Positive definiteness: for every , if and only if is the zero vector.
Optimal controlOptimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure.
Sequential spaceIn topology and related fields of mathematics, a sequential space is a topological space whose topology can be completely characterized by its convergent/divergent sequences. They can be thought of as spaces that satisfy a very weak axiom of countability, and all first-countable spaces (especially metric spaces) are sequential. In any topological space if a convergent sequence is contained in a closed set then the limit of that sequence must be contained in as well. This property is known as sequential closure.
Solution setIn mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities. For example, for a set {f_i} of polynomials over a ring R, the solution set is the subset of R on which the polynomials all vanish (evaluate to 0), formally {x\in R: \forall i\in I, f_i(x)=0} The feasible region of a constrained optimization problem is the solution set of the constraints. The solution set of the single equation is the set {0}.
