Self-adaptive and self-managing systems optimize their own behaviour according to high-level objectives and constraints. One way for human administrators to effectively specify goals for such optimization problems is using policies. Over the past decade, researchers produced various approaches, models and techniques for policy specification in different areas including distributed systems, communication networks, web services, autonomic computing, and cloud computing. Research challenges range from characterizing policies for ease of specification in particular application domains to categorizing policies for achieving good solution qualities for particular algorithmic techniques. The contributions of this thesis are threefold. Firstly, we give a mathematical formulation for each of the three policy types, action, goal and utility function policies, introduced in the policy framework by Kephart and Walsh. In particular, we introduce a first precise characterization of goal policies for optimization problems. Secondly, this thesis introduces a mathematical framework that adds structure to the underlying optimization problem for different types of policies. Structure is added either to the objective function or the constraints of the optimization problem. These mathematical structures, imposed on the underlying problem, progressively increase the quality of the solutions obtained when using the greedy optimization technique. Thirdly, we show the applicability of our framework through case studies by analyzing several optimization problems encountered in self-adaptive and self-managing systems, such as resource allocation, quality of service management, and Service Level Agreement (SLA) profit optimization to provide quality guarantees for their solutions. Our approach combines the algorithmic results by Edmonds, Fisher et al., and Mestre, and the policy framework of Kephart and Walsh. Our characterization and approach will help designers of self-adaptive and self-managing systems formulate optimization problems, decide on algorithmic strategies based on policy requirements, and reason about solution qualities. / Graduate / 0984