Influence of Lipschitz bounds on the speed of global optimization

• Main Authors: Remigijus Paulavičius, Julius Žilinskas
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2012-04-01
• Series: Technological and Economic Development of Economy
• Subjects: global optimization; Lipschitz optimization; Lipschitz bounds; branch and bound algorithm
• Online Access: http://www.bjrbe.vgtu.lt/index.php/TEDE/article/view/4678

Global optimization methods based on Lipschitz bounds have been analyzed and applied widely to solve various optimization problems. In this paper a bound for Lipschitz function is proposed, which is computed using function values at the vertices of a simplex and the radius of the circumscribed sphere. The efficiency of a branch and bound algorithm with proposed bound and combinations of bounds is evaluated experimentally while solving a number of multidimensional test problems for global optimization. The influence of different bounds on the performance of a branch and bound algorithm has been investigated.