Kubica B.J. Interval Methods for Solving Nonlinear Constraint Satisfaction, Optimization and Similar Problems: From Inequalities Systems to Game Solutions

Springer, 2019. — 164 p. [1st ed.]This book highlights recent research on interval methods for solving nonlinear constraint satisfaction, optimization and similar problems. Further, it presents a comprehensive survey of applications in various branches of robotics, artificial intelligence systems, economics, control theory, dynamical systems theory, and others. Three appendices, on the notation, representation of numbers used as intervals’ endpoints, and sample implementations of the interval data type in several programming languages, round out the coverage.Front Matter.
Introduction.
Interval Calculus.
Bounding Derivatives by Algorithmic Differentiation.
Branch-and-Bound-Type Methods.
Solving Equations and Inequalities Systems Using Interval B&Bt Methods.
Solving Quantified Problems Using Interval Methods.
Parallelization of B&BT Algorithms.
Interval Software, Libraries and Standards.
Applications of Interval B&BT Methods.
Back Matter.