The Wind Farm Layout Optimization (WFLO) problem has attracted a lot of attention from researchers and industry practitioners, as it has been proven that better placement of wind turbines can increase the overall efficiency and the total revenue of a wind farm. Although the engineering wake models are commonly used for layout optimization, the literature seems to have settled on using metaheuristics and stochastic optimization methods. In the present study, we show the effectiveness of non-linear mathematical programming in solving continuous-variable WFLO problems by utilizing exact gradient information of the problem's objective and constraints. Moreover, mathematical models for handling land -use constraints are developed to solve highly constrained practical problems. For demonstration purposes, the results were compared with those obtained by a genetic algorithm, using a set of test cases that have been frequently used in the WFLO literature. Additional test cases with higher dimensionality, significant land -availability constraints and higher wind farm turbine densities (i.e., turbines per square kilometer) are devised and solved to show the merits of the proposed approach. Our results show the superiority of mathematical programing in solving this problem, as evidenced by the resulting wind farm efficiency and the computational cost required to obtain the solutions. (C) 2016 Elsevier Ltd. All rights reserved.