Interval Arithmetic Based Optimization in Nonlinear Regression

Nonlinear Transformations for Simplifying Optimization Problems

A new implementation of a symbolic simplification algorithm is presented together with extended theoretical results that support the underlying method for constrained nonlinear optimization problems. The program is capable to automatically recognize simplification transformations, and to detect implicit redundancy in the objective function or in the constraint functions. We have also discussed ...

Lp-based Strategy for Modeling and Optimization Using Interval Methods

The interval-Newton approach provides the power to solve nonlinear equation solving and global optimization problems with complete mathematical and computational certainty. The primary drawback to this approach is that computation time requirements may become quite high. In this paper, a strategy for using linear programming (LP) techniques to improve computational efficiency is considered. In ...

Arithmetic Aggregation Operators for Interval-valued Intuitionistic Linguistic Variables and Application to Multi-attribute Group Decision Making

The intuitionistic linguistic set (ILS) is an extension of linguisitc variable. To overcome the drawback of using single real number to represent membership degree and non-membership degree for ILS, the concept of interval-valued intuitionistic linguistic set (IVILS) is introduced through representing the membership degree and non-membership degree with intervals for ILS in this paper. The oper...

Exact soultion of full interval linear equation AX=B based on Kaucher arithmetic

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

IBEX is a 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 ...