Optimization of Maintenance Planning for Multi-Component Systems, and Primal-Dual Convergence Characterizations in Convex Optimization

Abstract: This thesis considers two topics within mathematical programming. The first topic is an investigation into the behaviour of primal-dual subgradient algorithms with primal ergodic averaging in the case where it is not known a priori whether the primal program is consistent or not. In particular it is shown that, in the case of convex primal programs, relevant information can be obtained regardless of the consistency of the primal program. The second topic is that of maintenance optimization of multi-component systems. It is that mathematical programming techniques of the combinatorial type can be used successfully to plan maintenance of multi-component system where components are interdependent in a non-trivial way.