RT Journal Article
T1 On Dealing with Minima at the Border of a Simplicial Feasible Area in Simplicial Branch and Bound.
A1 G.-Tóth, Boglárka
A1 Hendrix, Eligius María Theodorus
A1 Casado, Leocadio G.
A1 Messine, Fréderic
K1 Programación matemática
AB We consider a simplicial branch and bound Global Optimization algorithm, where the search region is a simplex. Apart from using longest edge bisection, a simplicial partition set can be reduced due to monotonicity of the objective function. If there is a direction in which the objective function is monotone over a simplex, depending on whether the facets that may contain the minimum are at the border of the search region, we can remove the simplex completely, or reduce it to some of its border facets. Our research question deals with finding monotone directions and labeling facets of a simplex as border after longest edge bisection and reduction due to monotonicity. Experimental results are shown over a set of global optimization problems where the feasible set is defined as a simplex, and a global minimum point is located at a face of the simplicial feasible area.
PB Springer Nature
YR 2024
FD 2024-07-22
LK https://hdl.handle.net/10630/35163
UL https://hdl.handle.net/10630/35163
LA eng
NO Tóth, B.G., Hendrix, E.M.T. , Casado, L.G and  Messine, F. (2024), On dealing with minima at the border of a simplicial feasible area in simplicial Branch and Bound , Journal of Optimization Theory and Applications, 203, 1880-1909
NO This work has been funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, Grant PID2021-123278OB-I00 of the Spanish ministry of Science and Innovation and grant TKP2021-NVA-09 of the Ministry for Innovation and Technology, Hungary.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 19 ene 2026