Necessary and sufficient optimality conditions for the extended trust region subproblem

We consider the problem of minimizing an extended trust region sub-problem (eTRS) in which the trust region ball intersects with a single linear inequality constraint. Using a variation of S-Lemma, we present a new necessary and sufficient global optimality conditions for (eTRS). Then a new SOCP/SDP formulation is introduced for the problem.

کلیدواژه ها:

Extended trust region subproblem ، global optimization ، S-lemma ، semidefinite optimization relaxation