Revisiting the upper bounding process in a safe Branch and Bound algorithm

TL;DR

This paper introduces a new Newton-based strategy to efficiently compute accurate feasible points and upper bounds in safe Branch and Bound algorithms for continuous problems, improving their effectiveness.

Contribution

It presents a novel approach leveraging linear relaxations and Newton's method to enhance feasible point approximation in safe Branch and Bound algorithms.

Findings

Effective in computing accurate feasible points

Improves upper bound estimation efficiency

Demonstrated on Coconuts benchmarks

Abstract

Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new strategy to compute very accurate approximations of feasible points. This strategy takes advantage of the Newton method for under-constrained systems of equations and inequalities. More precisely, it exploits the optimal solution of a linear relaxation of the problem to compute efficiently a promising upper bound. First experiments on the Coconuts benchmarks demonstrate that this approach is very effective.