During the last 40 years, simplicial partitioning has been shown to be highly useful, including in the field of nonlinear optimization, specifically global optimization. In this article, we consider results on the exhaustivity of simplicial partitioning schemes. We consider conjectures on this...

In this paper, we propose a structured trust-region algorithm combining with filter technique to minimize the sum of two general functions with general constraints. Specifically, the new iterates are generated in the Gauss-Seidel type iterative procedure, whose sizes are controlled by a...

We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an...

The main goal of this note is to give a counterexample to the Triality Theorem in Gao and Ruan (Math Methods Oper Res 67:479–491, 2008 ). This is done first by considering a more general optimization problem with the aim to encompass several examples from Gao and Ruan (Math Methods Oper Res...

The main goal of this note is to give a counterexample to the Triality Theorem in Gao and Ruan (Math Methods Oper Res 67:479–491, <CitationRef CitationID="CR2">2008</CitationRef>). This is done first by considering a more general optimization problem with the aim to encompass several examples from Gao and Ruan (Math Methods Oper Res...</citationref>