A mixed algorithm for smooth global optimization

Document Type : Research Article


Laboratory of Fundamental and Numerical ‎Mathematics (LMFN), Department of Mathematics, University Ferhat Abbas Setif 1, 19000 ‎Setif, Algeria


This paper presents a covering algorithm for solving bound-constrained global minimization problems with a differentiable cost function. In the proposed algorithm, we suggest to explore the feasible domain using a one-dimensional global search algorithm through a number of parametric curves that are relatively spread and simultaneously scan the search space. To accelerate the corresponding algorithm, we incorporate a multivariate quasi-Newton local search algorithm to spot the lowest regions.  The proposed algorithm converges in a finite number of iterations to an $\varepsilon$-approximation of the global minimum. The performance of the algorithm is demonstrated through numerical experiments on some typical test functions.