Constraints have been influential in the construction of GUIs for a long time. In GUIs the main usage of constraints is to define the layout of the widgets. Resizing behavior is very important in GUIs because areas have domain specific parameters such as form the resizing of windows. If we use linear objective function and resize window then error is not distributed equally. To distribute the error equally we introduce a quadratic objective function. Various algorithms are widely used for solving linear constraints and quadratic problems in a number of different scientific areas. The interior point and active set methods are most commonly used techniques to solve quadratic programming problems. Current constraint solvers designed for GUI layout do not use interior point methods for solving a quadratic objective function subject to linear equality and inequality constraints. In this paper, we compare performance aspects and the convergence speed of interior point and active set methods when they are implemented for graphical user interface layout. The performance and convergence of the proposed algorithms are evaluated empirically using randomly generated UI layout specifications of various sizes. The results show that the interior point algorithms perform significantly better than that of the QOCA-solver, which uses the active set method implementation for solving quadratic optimization.