This thesis describes a method for optimizing the performance of buildings. Design decisions made in early stages of the building design process have a significant impact on the performance of buildings, for instance, the performance with respect to the energy consumption, economical aspects, and the indoor environment. The method is intended for supporting design decisions for buildings, by combining methods for calculating the performance of buildings with numerical optimization methods. The method is able to find optimum values of decision variables representing different features of the building, such as its shape, the amount and type of windows used, and the amount of insulation used in the building envelope. The parties who influence design decisions for buildings, such as building owners, building users, architects, consulting engineers, contractors, etc., often have different and to some extent conflicting requirements to buildings. For instance, the building owner may be more concerned about the cost of constructing the building, rather than the quality of the indoor climate, which is more likely to be a concern of the building user. In order to support the different types of requirements made by decision-makers for buildings, an optimization problem is formulated, intended for representing a wide range of design decision problems for buildings. The problem formulation involves so-called performance measures, which can be calculated with simulation software for buildings. For instance, the annual amount of energy required by the building, the cost of constructing the building, and the annual number of hours where overheating occurs, can be used as performance measures. The optimization problem enables the decision-makers to specify many different requirements to the decision variables, as well as to the performance of the building. Performance measures can for instance be required to assume their minimum or maximum value, they can be subjected to upper or lower bounds, or they can be required to assume certain values. The optimization problem makes it possible to optimize virtually any aspect of the building performance; however, the primary focus of this study is on energy consumption, economy, and indoor environment. The performance measures regarding the energy and indoor environment are calculated using existing simulation software, with minor modifications. The cost of constructing the building is calculating using unit prices for construction jobs, which can be found in price catalogues. Simple algebraic expressions are used as models for these prices. The model parameters are found by using data-fitting. In order to solve the optimization problem formulated earlier, a gradient-free sequential quadratic programming (SQP) filter algorithm is proposed. The algorithm does not require information about the first partial derivatives of the functions that define the optimization problem. This means that techniques such as using finite difference approximations can be avoided, which reduces the time needed for solving the optimization problem. Furthermore, the algorithm uses so-called domain constraint functions in order to ensure that the input to the simulation software is feasible. Using this technique avoids performing time-consuming simulations for unrealistic design decisions. The algorithm is evaluated by applying it to a set of test problems with known solutions. The results indicate that the algorithm converges fast and in a stable manner, as long as there are no active domain constraints. In this case, convergence is either deteriorated or prevented. This case is described in the thesis. The proposed building optimization method uses the gradient-free SQP filter algorithm in order to solve the formulated optimization problem, which involves performance measures that are calculated using simulation software for buildings. The method is tested by applying it to a building design problem involving an office building. The results indicate that the method is able to find design decisions that satisfy all requirements to the decision variables and performance measures. Furthermore, the time needed by the algorithm for solving the optimization problem is acceptable. There are still a number of unresolved issues regarding the building optimization method, which are suggested as further research in the field of building optimization methods. Two papers are included in Appendix concerning so-called space mapping algorithms. These algorithms are relevant for developing fast and reliable building optimization methods.