On a particular quadratic network problem
This paper studies the quadratic function defined by \(f(x)=g(x)+h(x)\) over a convex polyhedron X, where g(x) is a quadratic form. The mathematical background related to quadratic forms and multiobjective programming is presented in Section 2. The problem is studied assuming that g(x) is a positive semidefinite quadratic form. A nonlinear problem arises and three theorems characterize it and an algorithm is given for solving it. A procedure is proposed for implementing the algorithm. The negative semidefiniteness of g(x) fixes another problem which is similarly studied. Two theorems are given and another algorithm is proposed. The study of the indefinite case is accomplished in three theorems that fix the corresponding theory but no algorithm is proposed. The algorithms are multiobjective programming based.
scientific article; zbMATH DE number 4016605