spatial branch and bound – Page 2

On convex relaxations of quadrilinear terms

Published: 2009/05/08, Updated: 2009/06/05

(Mixed) Integer Nonlinear Programming, Global Optimization bilinear, convex relaxation, global optimization, mixed-integer nonlinear programming, quadrilinear, reformulation, spatial branch and bound, trilinear

The best known method to find exact or at least epsilon-approximate solutions to polynomial programming problems is the spatial Branch-and-Bound algorithm, which rests on computing lower bounds to the value of the objective function to be minimized on each region that it explores. These lower bounds are often computed by solving convex relaxations of the … Read more

Branching and bounds tightening techniques for non-convex MINLP

Published: 2008/08/02, Updated: 2008/08/25

(Mixed) Integer Nonlinear Programming, Global Optimization global optimization, mixed-integer nonlinear programming, nonconvex optimization, spatial branch and bound

Many industrial problems can be naturally formulated using Mixed Integer Nonlinear Programming (MINLP). Motivated by the demand for Open-Source solvers for real-world MINLP problems, we have developed a spatial Branch-and-Bound software package named COUENNE (Convex Over- and Under-ENvelopes for Nonlinear Estimation). In this paper, we present the structure of couenne and discuss in detail our … Read more