Semidefinite relaxations for semi-infinite polynomial programming

This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many constraints. Then we propose an exchange algorithm with SDP relaxations to solve SIPP problems with compact index set. At last, we extend the proposed method to SIPP problems with noncompact index set via homogenization. Numerical results show that the algorithm is efficient in practice.Comment: 23 pages, 4 figure

New Upper Bounds in the Second Kershaw's Double Inequality and its Generalizations

In the paper, new upper bounds in the second Kershaw’s double inequality and its generalizations involving the gamma, psi and polygamma functions are established, some known results are refined