The research report is focused on optimization algorithms with application to quality of service (QoS) routing. A brief theoretical background is provided for mathematical tools in relation to optimization theory. The rest of the report provides a survey of different types of optimization algorithms: several numerical methods, a heuristics and a metaheuristic. In particular, we discuss basic descent methods, gradient-based methods, particle swarm optimization (PSO) and a constrained-path selection algorithm called Self-Adaptive Multiple Constraints Routing Algorithm (SAMCRA).