On solving a class of fractional semi-infinite polynomial programming problems

In this paper, we study a class of fractional semi-infinite polynomial programming (FSIPP) problems, in which the objective is fraction convex and concave polynomial, constraints consist infinitely many inequalities. To solve such problem, first reformulate it to pair primal dual conic optimization reduce semidefinite (SDP) problems if can bring sum-of-squares structures into constraints. end, provide characteristic cone constraint qualification for guarantee strong duality also attainment solution its own interest. framework, present hierarchy SDP relaxations with asymptotic convergence FSIPP problem whose index set defined by finitely Next, four cases be reduced either single or finite sequence where at least one minimizer extracted. Then, apply approach corresponding multi-objective find efficient solutions.