(Georgia Institute of Technology, 2018-12-13)
Cohen, Raphael P.
The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. However, this cannot happen without addressing proper attention to the soundness of these algorithms. This PhD thesis discusses the formal verification of convex optimization algorithms with a articular emphasis on receding-horizon controllers. Additionally, we demonstrate how theoretical proofs of real-time optimization algorithms can be used to describe functional properties at the code level, thereby making it accessible for the formal methods community. In seeking zero-bug software, we use the Credible Autocoding scheme. We focused our attention on the ellipsoid algorithm solving second-order cone programs (SOCP). In addition to this, we present a floating-point analysis of the algorithm and give a framework to numerically validate the method.