  Constraints have played an important role in the construction of GUIs, where
they are mainly used 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 linear objective function is used and window
is resized then error is not distributed equally. To distribute the error
equally, a quadratic objective function is introduced. Different algorithms are
widely used for solving linear constraints and quadratic problems in a variety
of different scientific areas. The linear relxation, Kaczmarz, direct and
linear programming methods are common methods for solving linear constraints
for GUI layout. 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, performance aspects and the convergence speed of
interior point and active set methods are compared along with one most commonly
used linear programming method 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 the Simplex method and QOCA-solver, which uses the
active set method implementation for solving quadratic optimization.
