Global Optimization Based on Contractor Programming: An Overview of the IBEX Library

Abstract

IBEX is an open-source C++ library for constraint processing over real numbers. It provides reliable algorithms for handling non-linear constraints. In particular, roundoff errors are also taken into account. It is based on interval arithmetic and affine arithmetic. The main feature of IBEX is its ability to build strategies declaratively through the contractor programming paradigm. It can also be used as a black-box solver or with an AMPL interface. Two emblematic problems that can be addressed are: (i) System solving: A guaranteed enclosure for each solution of a system of (nonlinear) equations is calculated; (ii) Global optimization: A global minimizer of some function under non-linear constraints is calculated with guaranteed and reliable bounds on the objective minimum.

Conditional Quantitative Program Analysis

“…Linear integer constraints can be efficiently and exactly solved using Barvinok's algorithm [33] (with offthe-shelf implementations including Latte [34] and Barvinok [36]). Nonlinear constraints over numerical variables can rely on progress in convex analysis [56], interval constraint paving [35], [57], and the approximate methods developed in both program analysis [54], [58], [59] and statistical machine learning [60]. Model counting over string domains includes exact counters for regular languages [38], exact bound computation [37], and mixed string/numerical counters [61].…”

Certified detection of parallel robot assembly mode under Type 2 singularity crossing trajectories

“…The algorithm is implemented in C++ language and compiled using MinGW. The program uses the IBEX library [35] to perform interval computations. Experiments were carried out on a quad-core Intel i7 processor at 2.40 GHz.…”

A greedy approach for a rolling stock management problem using multi-interval constraint propagation

“…The inequality constraints are used to reduce the domain of the values through a set of methods called contractors (Chabert and Jaulin 2009). Atomic and meta-contractors can be considered as basic elements of a new paradigm called contractor programming in order to perform efficient global optimization algorithm (Ninin 2015) exploiting the properties of groups of constraints. In the next section of the paper we present a contraction method for the Path Scheduling Problem previously introduced.…”