An algorithm for indefinite quadratic programming with convex constraints (Q1180839)

The authors present a new branch-and-bound method for solving the following problem: \[ \min(f(x,y)=p^ T x+x^ T My+q^ T y: (x,y)\in S), \] where \(S\subset R^ n\times R^ m\) is a closed convex non-empty set, \(p\in R^ n\) and \(q\in R^ m\) are given vectors and \(M\) is a given \(n\times m\) matrix. The branching here is a simplex bisection and the bounding operation is connected with the solution of \((m+1)\) convex subprograms and in the case if \(S\) is a polyhedron these subprograms are even linear.