An SDP method for fractional semi-infinite programming problems with SOS-convex polynomials

In this paper, we study a class of fractional semi-infinite polynomial programming problems involving sos-convex functions. For such problem, by conic reformulation proposed in our previous work and the quadratic modules associated with index set, hierarchy semidefinite (SDP) relaxations can be constructed convergent upper bounds optimum obtained. introducing Lasserre’s measure-based representation nonnegative polynomials on set to reformulation, present new SDP relaxation method for considered problem. This enables us compute lower extract approximate minimizers. Moreover, defined infinitely many inequalities, obtain procedure construct sequence outer approximations which have representations (SDr). The convergence rate SDr are also discussed.