Problems with resource allocation constraints and optimization over the efficient set

The paper studies a nonlinear optimization problem under resource allocation constraints. Using quasi-gradient duality it is shown that the feasible set of the problem is a singleton (in the case of a single resource) or the set of Pareto efficient solutions of an associated vector maximization problem (in the case of $$k>1$$ resources). As a result, a nonlinear optimization problem under resource allocation constraints reduces to an optimization over the efficient set. The latter problem can further be converted into a quasiconvex maximization over a compact convex subset of $$\mathbb{R }^k_+.$$ Alternatively, it can be approached as a bilevel program and converted into a monotonic optimization problem in $$\mathbb{R }^k_+.$$ In either approach the converted problem falls into a common class of global optimization problems for which several practical solution methods exist when the number $$k$$ of resources is relatively small, as it often occurs. Copyright Springer Science+Business Media New York 2014