Note that the delay through the combinational component of sequential circuit is a lower bound on the cycle-time. The design is considered to be optimized if the combined minimization of area and maximization of performance are achieved. Circuit optimization involves multiple objective functions, where the optimization goals range from one to multiple objectives. In general, the optimization problem is difficult to solve, due to the discontinuous nature of the objective functions and to the discrete nature of the design space, i.e. of the set of feasible circuit implementation. Such problems are related to testing some properties of a model.
Optimization problems are at least as difficult to solve as the corresponding decision problems.
In a problem complexity analyses, only decision problems are considered, because they provide a lower bound on the complexity of the corresponding optimization problem. Due to the large complexity of digital circuits, discontinuous nature of the objective functions and to the discrete nature of the design space, the optimization problems in a circuits design cannot be solved with the analytical methods in most cases, but are usually solved using algorithmic approach. An exact algorithm always provides the exact solution, often called global optimum of the optimization problem. Unfortunately, some exact algorithms may have such a high computational cost that their use can be prohibitive on problems of typical size. Hence, there is a need for approximation algorithms, which are not guaranteed to find the exact solution of the optimization problem, but can provide good approximation of the exact solution, which may be valid for practical applications.