On the Maximization of a Concave Quadratic Function with Box Constraints

Maximization of A convex quadratic function under linear constraints

On Nonconvex Quadratic Programming with Box Constraints

Non-Convex Quadratic Programming with Box Constraints is a fundamental NP-hard global optimisation problem. Recently, some authors have studied a certain family of convex sets associated with this problem. We prove several fundamental results concerned with these convex sets: we determine their dimension, characterise their extreme points and vertices, show their invariance under certain affine...

A Concave Maximization Problem with Double Layers of Constraints on the Total Amount of Resources

This paper investigates a kind of resource allocation problem which maximizes a strictly concave objective function with double layers of constraints on the total amount of resources. Resources are distributed on a two-dimensional space, say, a geographical space with time flow, and are doubly constrained in the sense that the total amount is limited on the whole space and the subtotal amount i...

On the Maximization of a Concave

We introduce a new method for maximizing a concave quadratic function with bounds on the variables. The new algorithm combines conjugate gradients with gradient projection techniques, as the algorithm of Mor e and Toraldo (SIAM J. on Optimization 1, pp. 93-113) and other well-known methods do. A new strategy for the decision of leaving the current face is introduced, that makes it possible to o...

Determinant Maximization of a Nonsymmetric Matrix with Quadratic Constraints

This paper presents the problem of maximizing the determinant of a K-square real matrix B, subject to the constraint that each row bk of B satisfies b t kΓkbk ≤ 1, where Γ1, . . . , ΓK , are K given real symmetric positive definite matrices. Existence and uniqueness of the solution is discussed. An iterative algorithm, using a method of relaxation type, is proposed in order to solve this proble...