A new constrained ellipsoidal algorithm for nonlinear optimization with equality constraints

This paper presents a new algorithm for nonlinear optimization, the cone ellipsoidal algorithm (CEA), that is suitable for dealing with equality constraints and deterministically converges to the global solution in convex problems. The algorithm is based on the traditional ellipsoidal algorithm and on some new cone conditions. CEA simultaneously searches the objective function minimum and the problem feasible region. A case study is presented: the well-known TEAM 22 benchmark problem. The new algorithm finds a solution that is at least as good as the best solution that is known, with high computational efficiency.