Allocation of limited resources under quadratic constraints

Abstract The proper allocation/distribution of limited resources is a traditional problem with various applications. mathematical formulation such problems usually includes constraints describing the set feasible solutions ( ), from which (nearly) optimal or equilibrium solution should be selected. Often more difficult to determine than find solution. Alternatively, already known often makes it easier select In some other cases, any are same satisfactory, additional optimization needless. Accordingly, main only task in many cases itself. paper, new theorem proved for explicit expression properly assigned (dependent) variables by means (independent) system inequality and quadratic equality constraints. sum (nonnegative) can either prefixed not. may describe resource allocation tasks (possibly game-theoretical contexts) problems. Two lemmas supporting proof above mentioned theorem, nevertheless, they also considered independent results, help future derivations. Supported further lemma, practical algorithm derived assigning way variables, limited) arbitrary nonnegative values prescribed. Various examples provided facilitate utilizing results.