New Underestimator for Multivariate Global Optimization With Box Constraints

Abstract

The paper is concerned with the multivariate global optimization with box constraints. A new underestimator is investigated for twice continuously differentiable function on a box which is an extension of the approach developed in [5] for univariate global optimization.

New technique for solving multivariate global optimization

“…Nonlinear models are ubiquitous in many applications such as advanced engineering design, biotechnology, data analysis, environmental management, financial planning, process control, risk management, scientific modeling, etc. Their solution often requires a global search approach [18,4,22,3,21]. A variety of adaptive partition strategies has been proposed to solve global optimization models.…”

New technique for solving univariate global optimization

“…Nonlinear models are ubiquitous in many applications, e.g., in advanced engineering design, biotechnology, data analysis, environmental management, financial planning, process control, risk management, scientific modeling, and etc. Their solution often requires a global search approach [3,4,13,20,21,25,24,26].…”