We study certain semidefinite and linear programming lifting approximation schemes for computing the stability number of a graph. Our work is based on and refines De Klerk and Pasechnik’s approach to approximating the stability number via copositive programming (SIAM J. Optim. 12 (2002), 875–892). We show that the exact value of the stability number α(G) is attained by the semidefinite approxim...

In order to verify semialgebraic programs, we automatize the Floyd/Naur/Hoare proof method. The main task is to automatically infer valid invariants and rank functions. First we express the program semantics in polynomial form. Then the unknown rank function and invariants are abstracted in parametric form. The implication in the Floyd/Naur/Hoare verification conditions is handled by abstractio...

A robust truss optimization scheme, as well as an optimization algorithm, is presented based on the robustness function. Under the uncertainties of external forces based on the info-gap model, the maximization problem of robustness function is formulated as the optimization problem with infinitely many constraint conditions. By using a semidefinite relaxation technique, we reformulate the prese...